I carry tire chains almost always throughout the winter because of where I live and where I go.
For road driving in the High Country with camper on I have had enough traction from the camper to not need chains. I have the regular chain pattern (non V-bar) and have driven on roads with them but that was only because I did not want to take them off (all 4 tires) to go into town (about 8 miles) knowing that I would need to put them back on to return into the back woods. The roads were hard snow packed due to recent over night dump on top of already snow packed surfaces.) The chain pattern plus the weight of the camper did not make for a noisy or rough ride, but speeds were no higher than 30-40 MPH, but I really did not need them.
There was one time when I truly needed chains. It was to get out of a valley up a forest road on a hunting trip after a night snowfall. I had 'em on all 4 while keeping wheel speed up to get out. The weight of the camper was most certainly a huge advantage in this slippery situation on a snotty road... these conditions were what made wish I had the V-bar tread.
My opinions is this: If you are in backwoods snowy areas where chains may be needed on gravel, dirt or forest roads with deep snow and muddy/ snotty conditions then get V-bar patterns. If you are wanting chains for mostly paved or improved roads for "having them if you ever need them" then I think a regular chain pattern is better.
The weight of a camper will be to one's advantage as long as tires are in good shape for the conditions. Take into account the tire tread type. A more "street tread" obviously will affect traction. My experiences are based on a SRW truck... duallys may experience different results.
I HIGHLY recommend the cam adjusters! With these you almost do not need tensioners but I install these as well- I prefer the rubber ones.
I got mine from Tire Chains.com, good customer service and I recommend them. They also have good info on styles, prices as well as state laws, refer to:
Tire Chains.com