I think that BMP would win, but not as easily as y'all think.
People forgot that Kisame, Nagato, Sasori, Itachi and Kakuzu can use a Water Style Jutsus.
Nagato can use Chibaku Tensei, which not every member of BMP can destroy.
If one of BMP members start bleeding, then Hidan can pretty much kill him ( her ) with one right stab.
Deidara's C4 would kill every member of BMP including Big Mom.
Obito's Kamui would be pain in the ass for all of those, who has a bad CoO.
If we take Edo Tensei Akatsuki, then Akatsuki wins by the simple fact that BMP can't kill them.