Since the title says Hated Division Rival, this only comes down to the Dolphins/Patriots/Jets. I'd say it's probably the Fins overall. Yes, they have 20-0 in the 70s but the 90s was pretty back and forth with the Bills getting the better of it. Both teams had legendary QBs go through the 80s and 90s at the same time and there have been 5 playoff games between the two including a championship game.
As far as the Pats, I might hate them more, but, as far as it being a rivalry, the two teams really haven't been good at the same time for an extended period like the Bills/Fins have.