Is there a scheme where two cipher texts can be proven to have the same (unencrypted) content? Is there a scheme where two ciphertexts (encrypted with different keys) can be proven to have the same (plaintext) content without disclosing the plaintext or any private keys?  I assume that the public keys would need to be known.

This is for the purpose of detecting duplicated content on a server, without knowing the content.

This is probably impossible, but reading about homomorphic encryption leads me to think that it might be possible.
Consider that I, as an attacker, suspects what you're sending in your secret messages.  If what you propose were possible, then I could know your plaintext by comparing my encryption of what I thought you were sending to what you actually sent, and brute for variations until I could confirm what you had sent.  This would be VERY bad.  Therefore, I assume you understand why I hope what you want is impossible as you proposed.

What could be done, would be to hash the message before encrypting it, and then comparing the hashes... this would again, especially with rainbow tables, lead to what I said above... the ability to know the message without decrypting it.