Why is the anime version of Pikachu so much stronger than the game version of Pikachu? It's disappointing when you try to simulate the anime in the game by constructing your team as Ash does his.
It was probably because in the anime, Ash & Pikachu are the protagonists of the story. So it is only natural to have Pikachu very strong to defeat the antagonists. In the game however, it's up to the player's strategy on how to make Pikachu stronger. Furthermore, in the game, the player can choose any other Pokemon to train to be stronger, other than Pikachu.
In the first episodes, Pikachu wasn't that strong. The first fight against Rocko, wasn't a good fight, as Pikachu fainted quickly. The problem is, that the fights in the anime often have some factors that aren't covered in the games, like the spinklers of the first arena (you know, water and electricity. However, Ash never won that fight :D).
All in all, the anime-Pikachu isn't very strong. It's more like the enemies aren't very good (who are his enemies? Team Rocket? Ha.). Ash also never won one of the conferences(? why must they have different names? D:).
The main-reason why the anime-Pikachu may be a little stronger is, that it must be at least at level 100 now, after 5 regions (plus the orange-islands).