Up until recently, I always did them thumbless. I always do thumb around for regular bench, but for close-grip, I feel it a bit more in my tri's and slightly more power with thumbless. Tonight for my heaviest set I did thumb around, because I had kind of an almost scary incident a couple weeks ago. For close-grip, I unracked the bar, put the thumbless grip in place, but then the bar did a slight roll in the opposite direction and almost came out. My wrists had briefly lost stability or something. I fortunately recovered in time, but that was scary and could have been quite damaging.
So with the thumb around, I feel slightly less power and not as good of a drive, but I guess not a horrible difference. Not quite sure which way to go. Guess it is better to be safe and sacrifice a few pounds if need be.