Without a doubt hate the Pats more. The Jets don't ever pose a serious threat to us, long before Rex showed up they've just been full of hot air and easily deflated, their fans are just typical loudmouth, ignorant, idiots, BUT they are true loyal fans to follow such a **** franchise for so long, and I can respect that as we've certainly spent our fair share of time in the AFC's dumpster over the last few years.
The Patriots on the other hand play dirty (recall the Light/Crowder incident last year?), get all kinds of preferential treatment (don't bother arguing me NE homers, you won't get a response, the treatment is obvious) slap on the wrist penalties (if any) for anything ranging from unsportsmanlike conduct to taping other teams. Their fans for the most part are bandwagon post SB era followers, and I don't know about you guys but I find fans of most Boston area sports (Red Sox, Celtics, Pats) to be really annoying and obnoxious. Also as others have pointed out with BB's behavior, he is basically Rex Ryan with tact but he is obviously arrogant as hell and in my opinion just as big of a cry baby in his refusal to shake other coaches hand's following loses.
In a nut shell the whole NE franchise just pisses me of, where as the Jets just make me laugh because it's like getting to watch a train wreck in progress every year especially with their habit in recent years of starting with some momentum and then imploding, it's always fun to watch so much so that in a way it almost makes me like them.