Next Destinies is definitely going to be a game changer, there are such a large number of game changing cards, it's tough being able to tell where everything is going to fall. Currently EelZone, TyRam, CaKE, The Truth (Who came up with this name? I've been out of the loop for a bit and I have no idea who decided that this is an acceptable name for a deck), Chandelure, Six-Corners, and Durant are the decks that are seeing consistently high amounts of play across the board.
EelZone is going to remain around until Magnezone is either rotated, outclassed, or Eelektrik is subbed in for something else. The deck is quick and is benefiting from the addition of Zekrom EX, and a number of new trainers. While this deck may fall from its No.1 spot, it is still going to be a fantastic play.
TyRam has found its place in the metagame, as a top-tier deck, but not the best play. The deck will be benefiting from the new set, but not in the same way that EelZone is, Reshiram EX doesn't mesh with the strategy of TyRam (between recoil damage and Afterburner damage, you are going to have a serious dent in a 2-Prize Pokemon) although a Fliptini or an Evolite could help negate some of that possible damage. I foresee this deck remaining in the metagame, but in the end it is going to have some trouble adjusting to some of the other big hitting EX Pokemon.
CaKE probably won't be around after Next Destinies, while Kyurem's Glaciate may be a frightful attack now, Next Destinies is stepping up the Hit Points and the number of big hitters that are going to be around. Kyurem, Terrakion, and possibly Cobalion are all going to be in the next format, Kyurem's Outrage makes for a clean way to bring down Reshiram EX, Terrakion will be hitting Magnezone and Zekrom EX hard, and Cobalion will be able to lock uncharged EX into the active position, but these cards all hanging around in the same deck does not seem to be logical what with Mewtwo EX and Shaymin EX both being able to punch holes in the deck.
The Truth is going to get a number of new toys from this set. For a deck that relies on big Pokemon and abusing your opponent's inability to knock out your Pokemon, Next Destinies is a dream come true. I see this deck being another huge contender in the next format, but the exact components to the deck are as murky as always. Do Mewtwo EX and Regigigas EX find their way into the deck? Or is it Zekrom EX and Reshiram EX that are going to be the best choice for attackers now?
Chandelure is not going to make it into the next format. Bigger EX Pokemon are going to shirk off any damage that Chandelure places on them, while being able to knock out Chandelure with minimal difficulty.
Six Corners was a format counter, and a reactive deck, the idea of a reactive deck that tries to hit the weaknesses of the format will always be around, and with the number of powerful basics around as well it makes sense that there will be some sort of Meta counter deck. However as the format changes, so will Six-Corners, which runs the risk of being so completely warped by new additions from Next Destinies that it doesn't even resemble this deck.
Durant will probably remain a fringe deck. Durant gains Level Ball and Pokemon Center for support, but neither add a whole lot to the deck. While on the other hand, Durant is now going to have to deal with an increased number of Pokemon that are going to be able to knock it out. In the end Durant is going to remain an unreliable deck with a number of Auto-Losses, which will make it too unreliable of a deck for States.
So from the old format it seems that EelZone and TyRam are going to just be gaining a new attacker with either Reshiram EX or Zekrom EX, but other than that the decks will remain similar to what they are now. The Truth and Six Corners are going to remain in spirit, in that the overall strategy and key players within the deck are going to remain, but Next Destinies is going to reshape these decks.
The cards that are arriving from Next Destinies that are going to have influence are listed below...
Shaymin EX: Change to the Game 4/5 Shaymin EX is going to be adding another dimension to revenge attackers. With Prism Energy, Shaymin becomes an incredibly splashable card. You can even tech a single Grass Energy into your deck in case you start with your Shaymin EX and a Prism Energy in hand, so that you can utilize his first attack. While Shaymin is a little brittle to be having around, especially with it being worth two prizes, Shaymin is going to be a game-changer late in the game, especially if you are losing.
Kyogre EX: Change to the Game 0/5 Aside from its first attack, which is barely helpful in the first place, Kyogre EX is nothing special. Kyurem is a better Water-Type attacker, and it isn't hampered by being worth two prizes. While the second attack may seem usable, you would be better off using either Hydreigon or Kyurem to spread damage.
Mewtwo EX: Change to the Game 5/5 While Mewtwo is definitely overhyped, he is also going to change the game. For a single DCE you are going to be able to swing for 40+ damage, typically landing 60-80 damage. Mewtwo is able to land big hits on some of your opponent's biggest attackers. However Mewtwo is not going to be a deck in and of itself. Gardevoir, Eelektrik, Typhlosion, etc. are not good partners for Mewtwo and are much better when paired with a different attacker. Mewtwo and Gardevoir do make a decent pair, but just as Leafeon and Sceptile were back in the day, these two are not going to be a Tier 1 Deck. There is too much setup, too much danger with Mewtwo's two prizes, and just not enough energy acceleration for Mewtwo to be able to hit the bigger knock outs. Mewtwo is another great splashable tech, especially in any deck that runs DCE. Also as a sidenote, for anybody who claims that Mew Prime wins in the prize tradeoff between Mew and Mewtwo, you are wrong. You lose a Mew when you initially See Off (also if you are just playing a Mew + Jumpluff to counter Mewtwo you are going to have some consistency issues, and you are definitely not going to start with Mew often enough unless you dedicate an absurd amount of your deck just to Mew) and you also lose a Mew after you KO the Mewtwo, as your opponent is going to be able to hit the 60-80 needed to bring down Mew easily.
Level Ball: Change to the Game 4/5 Level Ball gives you the ability to search for any card with 90 or less HP. This gives decks another card that can grab basics early game. I feel reminiscent of the Ball-Engine from Mysterious Treasures, which means that there may be less of a dependency on Collector in a number of decks, which opens up a number of new Supporter options for the first turn.
EXP Share: Change to the Game 1/5 EXP Share does have some capabilities in this new format, but most decks either have more important uses for that space, the ability to recover energy already, or the deck would rather use Evolite. Overall I see EXP Share being a rare tech, or a helpful card in a rogue deck.
Skyarrow Bridge: Change to the Game 4/5 As mentioned in an above post, Skyarrow bridge breathes new life into Celebi Prime, Smeargle, and even Absol Prime. In fact any number of basic Pokemon are now able to retreat freely. However the amount of space that a deck should dedicate to this card in order to be able to retreat your starting Pokemon often is somewhat high. Two or three slots may need to be dedicated in order for your deck to be able to have an effective starter, but Switch will probably also be necessary to the deck what with the number of high-retreat Pokemon still in the format. While I can see this card changing the game, I also feel that a number of players will forego the benefits of the card in order to preserve deckspace.
Prism Energy: Change to the Game 5/5 Prism Energy is one of the biggest additions that will come from this set. Between Prism Energy and Rainbow Energy, it is possible to run a number of different types in a Basic-Pokemon oriented deck. Overall this card is outstanding for any deck that is going to focus heavily on a number of different basic Pokemon.
Chandelure: Change to the Game 1/5 Chandelure provides a decent way to spread damage, as well as a decent main attacker if necessary. However being a Stage 2 Pokemon Chandelure just is not going to see a lot of play. Perhaps a decent addition to Mew's arsenal, now it is possible for Mew to be a decent spreader.
Kyurem EX: Change to the Game 0/5 Kyurem EX is just a bad EX Pokemon. Both of its attacks are lackluster. Aside from a decent weakness and a great pile of HP, this card is simply not useful. Kyurem EX is outclassed by its regular counterpart, which is at least able to deal quick and easy damage from its Outrage attack.
Gardevoir: Change to the Game 2/5 Gardevoir is going to spawn a number of rogue decks, anything from Darmantian to Mewtwo EX can be used along with Gardevoir, but in the end the deck is just not going to be effective on a large scale. The setup is difficult and the damage output is high, but at the cost of a number of energy. I know Gardevoir will get play, but if the past is any indicator, this card will be hyped and played more than it deserves. It makes for a good strategy and a decent deck, but not anything that will shift the metagame.
Groudon EX: Change to the Game 3/5 Groudon is not an extraordinary card in its own right. Its first attack is pretty good, and its second attack is also usable. However its HP, typing, and resistance are what makes it shine. Groudon is one of the better Magnezone counters created. Groudon also works decently with either Lucario or Donphan Prime to make for a decent late-game sweeper. I would like to see Groudon receive some play, but I don't know how well Groudon can handle some of the other EX Pokemon.
Lucario: Change to the Game 1/5 Lucario is a decent card, one which will make for a good starting attacker in a Groudon deck. However aside from that, Lucario is just not a strong enough card in the new format to be able to stand on its own.
Bronzong: Change to the Game 1/5 Bronzong is not going to be widely played, if at all. However decks like The Truth, Groudon, Mewtwo, and Regigigas are going to try to preserve their EX Pokemon through healing, this makes Bronzong a possible play in order to prevent just that. However due to Catcher, I only see Bronzong being a possible play in Trainer Lock decks.
Regigigas EX: Change to the Game 2/5 Regigigas may be the next card to be big in The Truth. Regigigas uses DCE, has a large amount of HP, and a powerful Outrage-esque attack. Aside from that Regigigas may find his way into a couple other rogue decks, but nothing much past that.
Heavy Ball: Change to the Game 2/5 Heavy Ball has a small range of Pokemon that it can search, but being able to grab Magnezone Prime, Regigigas, Groudon, Kyogre, Kyurem, Mewtwo, and a number of other Pokemon warrants a look at this card.
Cilan: Change to the Game 2/5 Grabbing basic energy from your deck and placing them into your hand is a useful thing to have around, however there is a move to even more special energy, as well as a number of other ways to accelerate energy to begin with. A single tech of this card will be about the only play that it sees, but it does provide some decks with the extra energy that it may need.
Pokemon Center: Change to the Game 1/5 With Skyarrow Bridge rivaling this card for deckspace, Pokemon Center is only going to see play in the decks that really do need it. The Truth can use this card to keep the overall amount of damage on the field lower, while TyRam can use this card to avoid Afterburner damage.
Zekrom EX: Change to the Game 5/5 Zekrom EX is one of the best EX Pokemon to be released in Next Destinies. It works perfectly with EelZone, and it can deal a consistent 150 damage as long as you are able to keep the energy coming. Pachirisu and Shaymin are also possibilities to get the energy onto Zekrom.
Reshiram EX: Change to the Game 4/5 Reshiram EX is also going to have a huge influence on the format now working with TyRam, however the recoil damage from its attack and the damage from Afterburner make Reshiram a less reliable attacker than Zekrom.
Ultra Ball: Change to the Game 5/5 Probably one of the biggest cards to come out of the set, this card is also going to be played in almost every deck. Any deck that requires cards be placed into the discard pile, Even with decks that do not need cards in the discard pile, Ultra Ball is still one of the best ways to search for a Pokemon around, and at least one copy should make its way into every deck.
Random Receiver: Change to the Game 0/5 A quirky card that may show some usefulness down the line, Random Receiver is a way to make sure that you always have a supporter to play. This card would probably work better in a deck that runs a Ball-Engine so you don't run as high of a risk of hitting a useless Collector later in the game.
Conclusion
Overall I feel that this format is going to have decks that are built around EX Pokemon. EelZone will alter its playstyle to incorporate Zekrom EX, just as TyRam will for Reshiram. Groudon will be paired with Lucario for an early game attacker. Mewtwo will be paired with Gardevoir for energy acceleration. Regigigas will be paired with Vileplume and Reuniclus as the centerpiece for the new version of The Truth. Kyogre and Kyurem are not going to see much play, leading to a decent environment for Reshiram, although not a totally ideal environment as Kyurem NV will still be around. Shaymin and Mewtwo will both become common techs, and a number of trainers will work their way into the decks of the format.