But say you have two black boxes. The first uses Diffie-Hellman to exchange a key for subsequent AES encryption; the second exchanges a one time pad using quantum cryptography. What's the advantage of the second? In a passive attack (snooping alone), the snooper can't break Diffie-Hellman. In an active attack (man-in-the-middle), quantum crypto fails as well: I just put a machine in the middle that acts as A to B and B to A, receive one pad from A and send a completely different one to B, and go on my merry way, transparently reencrypting anything passing through.
You can't perform a man-in-the-middle attack with quantum crypto because the one-time-pads are exchanged in advance. You can't send an OTP with the message, you have to share it in a secure manner at some previous time. In the quantum crypto case, you would create and distribute the entangled particles ahead of time, then use the OTP to send a strong symmetric crypto key and encrypt your normal communication with that.
You can't intercept that one-time-pad key transmission because, if you did, you wouldn't be able to reproduce the OTP to re-encrypt your man-in-the-middle key to be sent to the other party. While quantum crypto doesn't prevent interference, it makes it impossible for the interference to not be noticed. That is its advantage.