Assuming that a 250 and 350 have the same options, the only differences I've seen:
-F350 has a rear block 1.5" taller. I recommend upgrading to a F350 rear block, ubolts, and installing a 1" coil spring spacer if you want to have a tall truck without going as far as a lift kit.
-F350 often has hydroboost brakes, F250 has vacuum brakes. Hydroboost stops with less peddle effort, and is used on the diesels. The Vacuum boost feels nicer in parking lots though, as it deosn't run off of your powersteering pump. Both stop a trailer equally, just feels a little different.
-the weight ratings are a bit different, I have to pay more to put tags on a F350.
Does that slid in camper really weigh 4000 pounds? Isn't that a bit heavy? Usually you'll be fine as long as you don't pack a ton of gear into your camper. I've seen people carry a complete dinner set for 7 people, and TV, microwave, etc. etc. Avoid overdoing it and it'll carry alot better.
I allmost flipped a 1 ton E350 van on I75 in Florida. I wasn't towing anything, but had 2000 pounds cargo, maybe 3000. I heard my rear tire let loose and the truck fishtailed violently about a foot left then right taking me into the next lane over as I tried to maintain speed and control, I didn't dare hit the brakes. I coasted to a stop. I get out and notice that the wheel isn't on the ground. THE ^&*#$%$$ TIRE STILL HAD AIR IN IT! ALL OF IT, NOT EVEN LEAKING! The tire just lost it's tread, still had the mm of rubber over the belts. The other rear tire was fine! That should not have been so hard to control. I believe that the E350's soft suspension, fat extended length whale tail, and short wheel base, was a huge part of the problem.
Adding air bags is allways an excellent idea. Keep that load level. No need for a compressor and switch kit. I've seen some people just use tire valves on each bag. Then just fill the bags at the gas station until your level. Simple, easy, cheap. If I called the shots, all my trucks at work would have air bags to help stiffen the truck up when towing. Really feels better towing with plenty of spring.
Converting or trading up to a dually is allways a great idea with slide in campers. Tires are often the weak link. Haveing 4 tires in the back helps a ton. Just get a F350 DRW.