Hands down the bolt action will win. But the BAR is awful accurate(the ones I've shot). Plenty accurate enough out to 300 yards or so where most people have no business shooting further anyway.
I am not at all convinced about needing quick follow up shots. I prefer to operate on the theory one shot one kill. But rest assured you are not getting a 7400 or mini 14 type accuracy with the BAR. Especially if you get a BOSS on it. Even if its not the braked BOSS.
As an anecdote to speed- ask a good bolt gun match shooter in rapid fire why they don't shoot a semi auto. They'll tell you with a semi they have to wait around for the action to cycle. Whereas with the bolt they can get on with it. Of course thats all bunk, but I'm awful good with a bolt gun and can get that second shot away awful fast. Just takes practice. In fact with something along the lines of 300-338, I've usually got the second round chambered as the gun comes down out of recoil.
You can do no harm buy shooting a BAR thats for sure.
Jeff