Lake Trio from Sinnoh (and Hisui) is arguably the most unique set of legendries in Pokemon History. Usually, legendary trios will have different typings. Azelf, Uxie and Mesprit are all Psychic-types, and thus share lots of the same moves.
The big difference between them, though, is the stats. Their spread drastically varies, making them very fun to rank.
Which legendary Pokemon is the best to battle with?
Back in Generation IV, the Pokemon assuredly would be ranked second. Uxie boasts some phenomenal defenses, which in most instances would make it a valuable member of this trio.
However, Uxie lost one of its best tools: Toxic. Since this is not a TM that can be used in the game, Uxie is unable to Toxic stall, which it would excel at with its huge defense and access to Recover.
That does not mean this Pokemon is not usable, though. It can still set up with Calm Mind and eventually be a huge threat. However, it will just take a lot of Calm Minds before it does meaningful damage.
Usually, Mesprit is considered the worst lake guardian, but since the changes to Uxie, the Pokemon looks better by comparison. It has enough defenses to Calm Mind set up, and enough offenses to do damage afterwards.
Granted, Mespirit’s natural movepool is still a little suspect. Double Hit will basically do no damage from this Pokemon, who, despite having a 105 base attack, wants to be a special attacker.
The only way Mesprit can do really well, though, is through the move shop, which gives it access to tons of coverage moves. Trainers can have their pick of Energy Ball, Shadow Ball, Ice Beam, Thunderbolt, and several other strong options.
Azelf outperforms the rest of the lake trio simply because it has almost ideal stats for an offensive Pokemon. Azelf gets 125 in both attacking stats and 115 base speed; that is enough to dominate most matchups.
The coverage that Azelf has is also the same as Mesprit and Uxie. However, Azelf is a better user of those coverage moves due to its stats. Azelf also gets one tool the other two don’t get: Nasty Plot.
Instead of using Calm Mind to boost its stats, Azelf can use Nasty Plot to get a double boost in special attack, followed by Thunderbolt or Ice Beam, which could levy a great deal of damage. With 125 base physical attack, Azelf could also make use of Explosion or Play Rough if desired.