There's actually a TV show thread devoted to this, inspired by a comment by shock-jock Howard Stern.
Of course, we have to get straight, are we talking about BSG (original) or BSG (new)? And which Enterprise?
The way I see it, the Capt. Kirk version of the Enterprise beats either of the BSGs, because, after all, it's Capt. Kirk! I mean, he beat the no-win Kobayashi Maru scenario . . .
On the other hand, the Capt. Harriman version of the Enterprise (from "Star Trek: Generation," aka Cameron in "Ferris Bueller's Day Off") would lose to either BSG without Capt. Kirk there to tell him what to do.
I'm skeptical of what Capt. Picard would do, perhaps attempt to resolve things peacefully, not realizing that the omnipotent force staging this fight has no interest in negotiations. Adm. Adama (the Edward James Olmos version) would probably get Picard to lower his shields and then fire off a couple of nukes at the Enterprise. Cmdr. Adama (the Lorne Green version) might actually try to negotiate as well, so that would end with both ships destroyed out of spite by the omnipotent force.
In all seriousness -- well, as much as this topic could possibly engender -- it seems to me that the thread commenters who side with the Enterprise are correct. Starfleet ships have transporters, and Galactica doesn't seem to have any shields that would stop the transporters from working. Just beam a tactical nuke into CIC and that's pretty much all she wrote. . . .