I remember when Ash fought the one dude with Darkrai and Latios in the Sinnoh League Finals (that guy was totally cheating too) and Pikachu held his own pretty well to the end (taking a Luster Purge to the face as he Volt Tackled into it rather epically).
I'm pretty sure abilities in the anime are more based on the trainer's style and situation. The fact that Pikachu has lost several times to gym leaders it should in-game easily cakewalk is testament to this fact.
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