which is correct
His enemies are just as powerful as him
His enemies are just as powerful as he
Moreover, "His enemies" are the subject of the sentence and therefore could be substituted with a Personal Pronoun, in this case, "They" whereas John (I'm referring to he/him to lessen confusion) is the object of the sentence, and can only be replaced by an objective pronoun (me, you, him, her, it, us, you, them), the case here being "him."
This is a comparison. They are just as powerful as he is.
1. is correct in traditional grammar, but is less used these days, because some people, like philo2009, think its old-fashioned, so they use 'him' instead.
I would also choose 2 for speech, and colloquially.
2. His enemies are just as powerful as him.