What is a single word describing a person who opposes another, yet is of equal status to them?

Can anyone give me a single word describing a person that is equal to somebody in status but an opponent to them at the same time?

"Rival" seems like a fitting choice.

I agree rival is good - better than counterpart, which doesn't necessarily imply opposition.

I think adversary also fits the bill, and perhaps carries more overtones of actual equality. A rival may simply be an opponent who's strong enough to compete at all, but if you have an adversary you know you're in for a tough fight where the outcome isn't at all certain.

Moriarty was Sherlock Holmes' arch-enemy.

Superman's nemesis was Lex Luthor.

"Your opposite number" is sometimes used.