Your choice needs to be based on two factors, what fits your hand best, and what turns your crank more.
If you can grip a large frame DA revolver so that the gun lines up with the center of your forearm and there is a space, half inch or less, between your middle finger and the fleshy part of your thumb, the DA may very well be the better choice. Your hand might be just too large to get a good hold of the factory SA grip, and some people don't like to have their pinky hang below the grip frame. The SRH has a good feature in that you can trim down a solid grip, as opposed to the rubber/wood things the gun comes with, to match your hand size with out the restriction of the metal grip frame common to other makes. I've always had difficulty fitting S&W N frame grips.
The SBH is a fine revolver, and a single action has certain benefits that I appreciate. For a wilderness carry gun that is likely to see hard use, a short barrelled SBH is hard to beat. It is chambered for a powerful cartridge, it is accurate, and in the view of some it handles recoil well. There is no crane to get sprung because the cylinder gets closed with carumba between the crane and the frame. I also like the continuous loading feature the single action has. I have an unaltered 3 screw SBH, so I carry an empty under the hammer. When I've fired my second shot, the empty chamber is now in line with the loading gate and can be loaded. From this point on you can continue to fire or reload as the situation dictates - so unlike a DA, the gun never needs to run dry.
There are many grip options for the SA Ruger. Some knowledgeable shooters claim there is better recoil management with a Bisley grip frame. I've yet to shoot one, so I can't comment, but enough folks seem to think so that it can't be disregarded. If I have a sore point with the SBH, it's that my middle knuckle occasionally gets painfully wrapped by the square back trigger guard. This problem can be resolved in a couple of ways namely; reshaping the trigger guard or choosing an aftermarket grip that fills the space between the back of the trigger guard and the grip frame.