Phil, they're both great actions, you won't go wrong with either.
I chose a 3-lug for my 6XC prone rifle for a few reasons. In no particular order:
Shorter bolt lift - this is nice when shooting prone since I keep the rifle in my shoulder, it just makes for a shorter motion. The BAT has a roller on the cocking pice that keeps the bolt lift effort low and smooth despite the shorter travel. Very nicely designed and made.
More even support to the case head - following Audette's theories on barrel whip caused by less than perfect case wall thickness variance being reduced with a 3-lug or 4 lug action. Count this as a theoretical plus.
I have several other 3-lug and 4-lug actions by other manufacturers and just sort of like that. I might never have bought a BAT if they didn't offer it; not that there's anything wrong with the 2-lug, it just didn't seem as interesting to me.
So, as you can see, mostly a personal preference sort of decision,with a bit of technical justification. So far I've shot three 500 yard matches with it, a 600-42X, a 596-39X and a 598-39X (all prone, 60 shot, iron sight, NRA matches). I'm satisfied with it.
http://riflemansjournal.blogspot.com/2010/08/equipment-breaking-in-bat.html