Honestly, I don't hate the Braves like I do the Phillies Marlins and Mets (in that order)
I think the biggest reason Nats fans don't hate the Braves as much as they do the Phillies or Marlins is because the Nats have been paradoxically successful against them even when we sucked. Not sure about the Mets though, I don't hate them so much as I like making fun of them. It's not that they haven't had great teams at times, they are just way too easy to mock.