Browsing two sites at the same time with Tor should really fuck up fingerprinting attacks if they are both being loaded through the same circuit at the same time. Some people download a big file in the background over Tor while they are surfing with Tor to try to fuck up fingerprinting attacks. I think that this would be useful but I have heard others argue that an attacker can filter this and still fingerprint you. I don't know for certain in either case but I certainly lean toward thinking that it will add protection from fingerprinting attacks. Surfing the clearnet directly and Tor at the same time will not help you though.