What do you mean by "power" exactly?
If you're talking about Ability and Moves, it gets a bit complicated. It seems like in the anime how powerful a Move is depends on how strong the Pokemon is. Now there does seem like some indication that "upgraded" moves are stronger then there weaker forms (like Thundershock, Thunderbolt, and Thunder). Also some moves are over exaggerated how weak or strong they are, like Hyper Beam is made out to be an invincible beam of destruction which can O.H.K. your Pokemon.
As for Abilities, they only seem to exist when they are convenient. A good example is with Ash's Pikachu who has Static which has a chance to paralyze and opponent if the opponent attacks Pikachu with a physical attack. But ALL the times Pikachu has been hit by a physical, it never paralyzes the opponent. Static has only activated two times (that I could find on Bulbapedia) in the entire series, once in AG070 "Balance of Power" paralyzing Norman's Vigoroth and again in DP132 "Evolving Strategies!" paralyzing Paul's Ursaring.
Even Resistance is sometimes ignored, the most famous is Electric-type attacks (not just from Pikachu) damaging Ground-type attacks and Normal-type & Ghost-type attacks damaging each others.