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Obviously, it's difficult to choose from just stats. Next up, we'll check their movesets and typeage. Things in bold mean the Pokémon gets STAB for that attack. Italics means that this Pokémon can use this attack well in correlation with its stats.
Vaporeon
Spoiler:
Type: Water
Weak to: Grass, Electric
Resistant to: Steel, Fire, Ice, Water (if Mold Breaker is used)
Immune to: Water (if Mold Breaker is not used)
Attacks Tackle
Tail Whip
Helping Hand
Sand-Attack Water Gun
Quick Attack
Bite Aurora Beam Aqua Ring
Last Resort
Haze
Acid Armor Hydro Pump Muddy Water
Jolteon
Spoiler:
Type: Electric
Weak to: Ground
Resistant to: Flying, Steel, Electric (if Mold Breaker is used)
Immune to: Electric (if Mold Breaker is not used)
Type: Fire
Weak to: Ground, Rock, Water
Resistant to: Bug, Steel, Grass, Ice, Fire (if Mold Breaker is used)
Immune to: Fire (if Mold Breaker is not used)
Attacks Tackle
Tail Whip
Helping Hand
Sand-Attack Ember Quick Attack Bite Fire Spin Fire Fang Last Resort
Smog
Scary Face Fire Blast
Lava Plume
Espeon
Spoiler:
Type: Psychic
Weak to: Bug, Ghost, Dark
Resistant to: Fighting, Psychic
Immune to: None
Attacks
Tackle
Tail Whip
Helping Hand
Sand-Attack Confusion
Quick Attack Swift Psybeam Future Sight
Psych-Up
Last Resort Psychic
Morning Sun
Power Swap
Umbreon
Spoiler:
Type: Dark
Weak to: Fighting, Bug
Resistant to: Ghost, Dark
Immune to: Psychic (Normal if Miracle Eye is used)
Attacks Tackle
Tail Whip
Helping Hand
Sand-Attack Pursuit
Quick Attack
Confuse Ray Faint Attack
Assurance
Last Resort
Mean Look
Screech
Moonlight
Guard Swap
Leafeon
Spoiler:
Type: Grass
Weak to: Flying, Poison, Bug, Fire, Ice
Resistant to: Ground, Water, Grass, Electric
Immune to: None
Attacks Tackle
Tail Whip
Helping Hand
Sand-Attack Razor Leaf
Quick Attack
Synthesis Magical Leaf
Giga Drain Last Resort
GrassWhistle
Sunny Day Leaf Blade
Swords Dance
Glaceon
Spoiler:
Type: Ice
Weak to: Fighting, Rock, Steel, Fire
Resistant to: Ice
Immune to: None
Well, by that we can clearly see that all of them have a disadvantage over at least one Pokémon. Jolteon seems to have the upperhand, however only having Leafeon resistant to its Electric-type attacks. Jolteon can easily take out Vaporeon and Glaceon (with Electric-type attacks and a Double Kick, respectively). Of course, Umbreon can beat Espeon due to a major advantage, but it would be taken out easily by Jolteon's Double Kick. Flareon can KO Leafeon and Glaceon, so then it would come down to a Flareon vs. Jolteon battle.
Jolteon is much faster, but more suspetible to Flareon's attacks due to low defenses. Both have the same HP, so that will do us no good to compare.
But because so many of Jolteon's STAB attacks are also boosted by its high special attack, making them easily three times as powerful, I'd have to put my money on Jolteon.
Fire seems to deem an edge advantage over lightning which is what makes it so interesting. Flareon has a much higher attack, but as Shinji pointed out, it would be no use if Jolteon is too fast that Flareon can't lay a hit on it. It would be an interesting battle though for sure. All the evolutions are very cool and powerful at that. I don't think you can go wrong with any of them. :)
Ok, I tried summarising each of the evolutions too:
Spoiler:
Vaporeon can be super effective against:
Espeon (Bite)
Flareon (Hydropump)
Leafeon (Aururo Beam)
Vaporeon's advantage: V.High HP, High S.ATK, Can use Muddy water (High damage and lowers accuracy), Can Freeze, Can use Aqua Ring.
Jolteon can be super effective against:
Vaporeon (Thunder)
Umbreon (Double Kick)
Leafeon (Pin Missile)
Espeon (Pin Missile)
Jolteon's advantage: High Speed, High S.ATK, Can Paralyze.
Flareon can be super effective against:
Leafeon (Fire Blast)
Glaceon (Fire Blast)
Espeon (Bite)
Flareon's advantage:.V.High ATK, High S.ATK, Can Burn, Can Poison, Can use Physical and Special attacks well.
Espeon can be super effective against:
Leafeon (Psychic)
Espeon's advantage: High Speed, V.High S.ATK, Can use Morning Sun, Can Confuse, Ability: Syncronise.
Umbreon can be super effective against:
Espeon (Faint attack)
Umbreon's advantage: High DEF, V.High S.DEF, Can use Moonlight, Can confuse.
Leafeon can be super effective against:
Vaporeon (Leaf Blade)
Leafeon's advantage: High ATK, V.High DEF, Can put to Sleep, Can use Synthesis/Giga Drain, Can use Sunny Day, Ability: Leaf Guard.
Glaceon can be super effective against:
Leafeon (Blizzard)
Espeon (Bite)
Glaceon's advantage: High DEF, V.High S.ATK, Can Freeze, Can use Hail, Can use Mirror Coat.
From that I think its safe to eliminate Leafeon due to too many having type advantages over it (4).
The other however are too close to call.
If you put it down to who goes first than Espeon and Jolteon get to attack first, that can potentially knock out Umbreon or Vaporeon (With Leafeon long gone XDD), however Vaporeon might have enough time to survive.
Although Espeon only has a type advantage to Leafeon it has the highest (with Glaceon) S.ATK and a good arsenal of attacks too. Therefore it could probably take out Any with a poor S.DEF in two hits.
Vaporeon, Espeon, Leafeon and Umbreon all have healing moves that could give them an advantage. Glaceon has Mirror coat which could take out many of the others as most would be using Special Attacks.
Flareon in the mean time, having an normal attack base, is fanging the others from behind and possibly burning OR poisoning them with Smog. Meaning meanwhile the others are slowly losing health. Vaporeon could then counter with a muddy water, taking down everyone's accuracy and giving it the advantage, with low accuracy Thunder is unlikely to hit (especially if Leafeon used sunny day before it got K.O'd) and so Vaporeon now has no major weaknesses).
There are so many ways it could turn out XD But judging from their move pools I think Vaporeon has the upper hand.
Ok, I tried summarising each of the evolutions too:
Spoiler:
Vaporeon can be super effective against:
Espeon (Bite)
Flareon (Hydropump)
Leafeon (Aururo Beam)
Vaporeon's advantage: V.High HP, High S.ATK, Can use Muddy water (High damage and lowers accuracy), Can Freeze, Can use Aqua Ring.
Jolteon can be super effective against:
Vaporeon (Thunder)
Umbreon (Double Kick)
Leafeon (Pin Missile)
Espeon (Pin Missile)
Jolteon's advantage: High Speed, High S.ATK, Can Paralyze.
Flareon can be super effective against:
Leafeon (Fire Blast)
Glaceon (Fire Blast)
Espeon (Bite)
Flareon's advantage:.V.High ATK, High S.ATK, Can Burn, Can Poison, Can use Physical and Special attacks well.
Espeon can be super effective against:
Leafeon (Psychic)
Espeon's advantage: High Speed, V.High S.ATK, Can use Morning Sun, Can Confuse, Ability: Syncronise.
Umbreon can be super effective against:
Espeon (Faint attack)
Umbreon's advantage: High DEF, V.High S.DEF, Can use Moonlight, Can confuse.
Leafeon can be super effective against:
Vaporeon (Leaf Blade)
Leafeon's advantage: High ATK, V.High DEF, Can put to Sleep, Can use Synthesis/Giga Drain, Can use Sunny Day, Ability: Leaf Guard.
Glaceon can be super effective against:
Leafeon (Blizzard)
Espeon (Bite)
Glaceon's advantage: High DEF, V.High S.ATK, Can Freeze, Can use Hail, Can use Mirror Coat.
From that I think its safe to eliminate Leafeon due to too many having type advantages over it (4).
The other however are too close to call.
If you put it down to who goes first than Espeon and Jolteon get to attack first, that can potentially knock out Umbreon or Vaporeon (With Leafeon long gone XDD), however Vaporeon might have enough time to survive.
Although Espeon only has a type advantage to Leafeon it has the highest (with Glaceon) S.ATK and a good arsenal of attacks too. Therefore it could probably take out Any with a poor S.DEF in two hits.
Vaporeon, Espeon, Leafeon and Umbreon all have healing moves that could give them an advantage. Glaceon has Mirror coat which could take out many of the others as most would be using Special Attacks.
Flareon in the mean time, having an normal attack base, is fanging the others from behind and possibly burning OR poisoning them with Smog. Meaning meanwhile the others are slowly losing health. Vaporeon could then counter with a muddy water, taking down everyone's accuracy and giving it the advantage, with low accuracy Thunder is unlikely to hit (especially if Leafeon used sunny day before it got K.O'd) and so Vaporeon now has no major weaknesses).
There are so many ways it could turn out XD But judging from their move pools I think Vaporeon has the upper hand.
Just one thing, Leafeon isn't weak to Psychic :P
And judging by attacks, it probably could KO the other Eeveelutions by focusing on their weaker stat - Defence.
After all, it hits everyone apart from Flareon for at least neutral damage, though Flareon slaughters it immediately. oh well ^^
Plus Jolteon has highest speed it goes first thunder STAB bye bye Vaporeon if it was holding Magnet even stronger i would change my vote if i could to Jolteon but i cant plus if it was the anime Vaporeon could just melt into water and attack Jolteon when Jolteon least expects an attack
But just because Jolteon is the strongest doesnt mean it is the best