Pikachu is more powerful, but Raichu has higher Speed, HP and Defenses, which makes it overall a better Pokemon for competitive than Pikachu. Raichu also learns more moves than Pikachu.

Don't let the Anime null your senses. Raichu IS stronger, tougher and more durable than Pikachu in the games. The only down side is that Raichu can't use the Light Ball but regardless it still has higher total base stats. However, it would have lower Attack and Sp. Attack, so Pikachu would generally be the better sweeper.