Just that, for me, "Bird of Prey" never sounded very Klingon to me. It always felt like it suggested a bird hunting and stalking its kill, waiting for the right moment to strike. IN Trek terms, Romulans creeping up under cloak, then revealing themselves long enough to swoop in for the kill. Klingons, on the other hand, just go in and conquer or blast the shit out of you, so "Battle Cruiser" seemed more appropriate.
But, yeah, with TSFS, the damage was done, and future Trek's ran with it. Klingons didn't get "warbirds" until the Abrams Trek movie. Until then, it was a huge, Next Gen era Romulan ship.