My wife and I spend about 150 nights a year out on the road in either our 5th wheel or our truck camper, usually is some type of campground, be it a private or government one. Over the last couple of years I have been taking notice of what the most popular trucks being used to pull trailers or haul truck campers. By and far, the most popular truck being used would be the Ford F350 SRW. I would guess I will see 10 SRW Fords for every one DRF Ford in the campgrounds, with their rigs. While a DRW may be theoretically more stable, usage shows me, that the SRW are very adequate for most users. Many tow trucks live a dual life, and are either a work truck at home or a daily driver. Some trucks only are used to tow a trailer or haul a truck camper it would seem. I would just guess that 60% or more of all camping trailers and truck camper are being hauled by Fords with Chevy and Dodge splitting the remaining 40%.
My previous truck was a 3/4 ton Dodge Cummins, which I put 144,000 miles on it, most of those miles were towing or hauling our RVs. It was over loaded, especially with the truck camper. But with all the modifications I had installed on it, it was very stable on the road. However when the time came to replace the truck, I bought a one ton crew cab, 4 by, diesel DRW Chevy (I have very little brand loyalty) but not because of stability, but to get the increased GVW, going from 9,200 lbs on my Dodge to 13,000 lbs on the Chevy. Now I can haul my truck camper, the same one, and be about 1,500 lbs under GVW instead of that over. Also I went from a short wheel base to a long wheel base and that made more difference in directional stability, than did the dual rear wheels, IMHO. Driving the Dodge was a constant matter of correcting the steering as I went down the road, the Chevy just goes where I point it, seldom having to make the minuet steering corrections.
But the DRW is a pain in the rear to use as a daily driver, here in south Florida with the traffic we have, so I have a Jeep Wrangler for that job, where the previous Dodge did a lot of those miles. If we are not traveling with the Chevy, it only gets fired up on Wednesdays to run to Wal Mart, about 5 miles away, to keep all the fluids pumping. If I got rid of my truck camper and only had the 5th wheel, and needed to replace my truck, I would most likely go back to a SRW F350 Ford or equivalent sized Chevy or Dodge. My wife bought me a "stick on" for the back of my crew cab 4X4 Chevy, that says "Mine is bigger than yours" She centered it on the tail gate of the truck. LOL