You can go with a SRW or DRW, but the DRW will give you more choices in what camper you can carry. Both have about the same actual axle rating, but the DRW has OEM tire ratings that allow it to carry more.
A SRW will do better in adverse terrain conditions than a DRW. The DRW will pack mud or snow between the dual rear tires and reduce traction. The wide footprint and flotation of a DRW give it a slight advantage in sand. If you have either truck with 19.5" wheels, flotation (sand) will poor but other terrain is not a problem.
Many people will sing the praises of wide hips resulting in better stability, but I will argue that it has more to do with less stressed sidewalls (you now have twice as many rear tires) and heavier spring rate than the wider footprint. My 3/4t truck with 19.5's and some suspension help was very stable carrying a 4000 lb camper. My 1-1/2t truck does this without modification, but I'm at half my payload capacity until I upgrade my camper.