Super Contests and the removal of Diving. At least regular Contests didn't require you to be insanely good at timing touch screen taps or give you 3 judges that could completely screw you up if someone else happened to choose the same judge as you did(which is every single time ever). Diving is really self-explanatory. I love it when games give you more areas to explore.
Another change I don't like are the rivals. Blue and Silver were great, Wally was somewhat likable(though you only battle him like twice), May/Brendan are just...unrival-like, and Barry is just annoying. What happened to the mean rivals of the old days, that could easily kick you butt(as does often happen to me) and they know it. The newer ones are all "Pokemon are friends let's battle buddy oh hey I lost I guess I'll just train more" and it is annoying.
Plus, it seems with each new game they seem to recieve less character development. While Blue was never really that developed, he at least learned how to admit defeat by the time G/S came by. Silver is easily the most developed of the rivals, with a simple-but effective backstory(which is something that the newer games got right about rivals!), and he slowly grows to love and trust his Pokemon, culminating with him trying to return his starter to Elm and telling you to heal your Pokemon after losing to you at the Indigo Plateau(but very obviously having a hard time doing so, being new to being a nice person and all).
Wally did get some development, but it was simply rookie trainer wants to start raising Pokemon and becomes good at it after you help him. We never even get to see his Pokemon grow, just one battle against his Ralts and another in the Victory Road, his Pokemon now very high-leveled. What happened inbetween? Did they just forget about him temporarily so they could focus on May/Brendan? And those two(plus Barry)...they never change at all, save for a stronger team. Barry had one moment of self-doubt, then it was back to his normal, perky, annoying self.
...Well, that rant on the rivals was longer than I intended.