Well, I actually noticed a pattern:
- Uxie has high Defense stats
- Azelf has high Attack stats
- Mesprit has high Attack and Defense stats
All of Uxie's defense stats are at 130,
All of Azelf's attack stats are at 125,
While all of Mesprit's attack and defense stats are at 105.
Not much of a difference, really.
Azelf is a great offender, as it has high attack and defense stats as well as a high speed stat, so it'll be able to move first more often.
It seriously just depends on what you want, but since offense is like the only thing you need in in-game (that's why I love about it xD), I'd choose Azelf.
Hope I helped. :)
Source: Serebii's pages on them