An ex of mine read a few of the trades of this. It was originally written by Chuck Dixon. Then Gail Simone took over, and now Tony Bedard is on. I've flipped through a few issues, but haven't really sat down and read any of it in a big block. I did borrow some trades from her though, and I plan on sitting back and reading them when I get the chance. From the first Simone arc I glanced over, it seems to be pretty accessible. All you really need to know is that Babs is the brain and Dinah is the muscle, and they operate as a sort of A-Team style squad. I'll get back to you on it once I've dug a little deeper into the trades, if you still need answers in a while.
Anyway, I mentioned this to her the other day after seeing this thread, and from talking to her, my understanding is this. Dixon's run was decent comic adventure fare, like most of what Dixon churns out. It was basically Barbara Gordon and Black Canary kicking ***. Simone's run (56-108 ) is supposedly really, really good, which doesn't surprise me one bit. When Simone takes over, it goes from being a fairly typical "grrl power" book and becomes a rather intelligent espionage title. She starts rotating in a wild amount of well-characterized and somewhat obscure DC females and really just spins it into a high octane, smart spy book. I've heard Tony Bedard's stuff isn't all that great, but the Simone issues are supposed to be the sweet spot. My understanding is that Simone basically used Birds of Prey as a farm team, to take poorly or under-characterized female characters and expand them in a way that they could step up as more prominent personalities in the universe proper.
Someone who's actually read it can probably elaborate better than me. But I'd trust tossing down cash on practically anything Simone penned. She's an all-star.