It depends on a variety of things.
1:
Is this for competitive play or regular playthough?
This is the biggest question. Espeon probally is best for Competitive play when it has Wish+Magic Bounce (it's DW ability). This bounces back hazards (Spikes, Stealth Rock, ect.) or other annoying things (Spore, Toxic, ect.). Unless you have a Rain team, then Vaporeon (with Wish+Hydration [DW Ability]) can be quite the tank and heals it's own status problems. This let's it use Rest and then wake up right away, or not have to worry about being poisoned.
If it's just for regular playthough, then you should answer these other questions. I always try to answer these when I do a run though, and they can help you find just what you need.
2:
What game are you playing?
Depending on the game you are playing, you can only get certain evolutions.
I'm guessing it's Black or White, so you have access to the 7 current eeveeolutions.
3:
What pokemon did you start with?
For regular game play, EVs, DW abilities, ect. aren't really that important. Type matchup is what really makes or breaks a battle. You're team should have different types to cover weaknesses of others. If you started with Tepig, I wouldn't recomend getting Flareon.
i.e. In my LeafGreen run though, I chose Flareon because I started with Venusaur, already had a Gyarados (didn't want 2 water types), and wanted a Magneton as an electric type.
However, I'm guessing you already finished the game, and that it's not FR or LG.
So it doesn't matter unless you really want to add it to your in-game strongest team.
4:
What do you want it to do for your team?
Do you want it to cover a weakness? Do you want it be a game finisher? A support pokemon?
i.e. Vaporeon with Baton Pass+Acid Armor can help support the team by giving any member some extra defense if you're worried about them surviving strong attacks. Also the first three eeveelutions (Vaporeon, Jolteon, Flareon) are all immune to moves that match their type (Water, Electric, Fire) using their normal abilities. So (i.e.) if one of your strongest is weak to Fire, Flareon woul dbe a nice balenece since it's Flash Fire Ability prevents it from being hurt by Fire type moves.
I'm not sure if I'm allowed to post a link, but I would recomend checking Bulbapedia, as that site can give you each of their move sets and give you their base stats as well.
edit: If you just want it for collection, just go with your favorite, or whichever you think looks coolest shiny. I'd pick Umbreon.