For me it is easier to cock the right hammer first on the flush. If I need a second shot or multiple bird flush I reach up and cock the far hammer. To me the first shot is the most important. On waterfowl I will cock both barrels as the ducks approach the decoys. I hunt alone most of the time, if I have a partner in the boat/blind I cock the near barrel as I raise the shotgun. I have both sxs and o/u hammer guns.

After the first shot the rest are just noise.