Well perhaps, just like with people and animals in real life, a long period of no training or excercise caused the Pokémon to gradually grow weaker, and consequently lose some of it's levels. If I remember right, Eagun mentions somewhere in the game that it had been awhile since he and his Pikachu last battled, so maybe it's lower level reflects this.
Anyways, there are a lot of things in Pokémon that make little to no sense, but it's a game. It's allowed to be that way C:
This post says it all, really.
It's a minor, irrelvent point, really. IMO Pikachu got a little bit fat over the years (reflecting the not-updated model of Pikachu used since Stadium for Colo/XD incidently if I remember right - leastways not much at all), and Eagun forgot that Pikachu knows electric attacks, hence it losing as well.
What's somewhat interesting is that in XD it's level 15. Although it's probably safe to say it isn't necessarily the same Pikachu, as later on he has two each of Pichu, Pikachu and Raichu. Electric-rat obsession FTL.
But this is really just some the programmers went with, without seriously worrying about what level a legendary trainer Pokemon
should be at. The point of that scene is to show that you are teh pokeyman master by being able to do better than Eagun, and that Shadow Pokemon are powerful. Leastways, more powerful than that Pikachu. A level 80 or so Pikachu Quick Attacking would probably win, which isn't what was meant to happen in the scene.
Anyway, it seems a pointless thread, especially when the nail head has already been hit so...