You just made my head hurt. Wow, what a mess.
Now that I am thinking about it, it doesn't make sense that both races would have a bird theme going on with their vessels. They all ready had a confusing and messed up think going on here. I've got to give the new movie credit for screwing this up even more than it already was. Let's give a nice big round of applause for Mr. J. J. Abrams!
Looking at this page, http://home.comcast.net/~ststcsolda/klingons/klingons.html (scroll down until you get to all nice little pictures) that Bird of Prey design looks completely out of place among all the other Klingon ships. They all have a certain look to them, and that one particular design just doesn't match. Now seems very obvious to me that it was originally intended to be a Romulan vessel.
And I was wrong in my previous post about Warbird = Romulan; Bird of Prey = Klingon. Both Warbird and Bird of Prey are originally Romulan, as FF said. But that one model of Klingon ship is called a Bird of Prey. There was never a Klingon Warbird until J.J. Trek (except for what was fully admitted to be a writing error found in the Enterprise pilot).
The fanboyesque explaination for the Klingon ship being named a Bird of Prey and looking Romulan is that Romulans and Klingons traded technologies, which is also why the Klingons have Romulan cloaking devices. I am usually not a big fan of contrived fanboy-explain-away-every-inconsistency explaintions, but this one works quite effectively IMHO.