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As the 250 and 350 are rated to tow the same amount, then yes, both are capable of towing that much weight. If cost is no object, however, then go with the dually, because it will tow better; less sway, more stable. But how often are you going to be towing? Couple times a year, or all the time? If it's every once in a while, then I'd save the cash and go with the 250 and put up with the sway. If you're "towing for a living," then you'll kick yourself for not getting the dually.
With that much weight you will overload a F250 w/diesel. Remember 8800 GVW. A single wheel F350 is rated at 9900 GVW.
That might be a better choice. Although you may indeed need a dual wheel truck. Are you positive about the trailer weight? Is that wet or dry? Less expensive to get all the facts and buy once.
First of all don't believe the trailer manufacturer's info. They are rarely correct for whatever reason. If your coach is available have the dealer take it down and weigh it. Then go from there. My previous truck was a '99 F350 dually, beautiful when towing but it takes some getting used to otherwise. I went to an "03 F350 Supercab, short bed, 6.0 with a PullRite Super Slide hitch. It took about 9,000 miles of towing to get used to the difference. I'm trying to get Ford to buy back my '03. If I'm successful I'll go back to a supercab dually. Ford's new transmission is awesome, the TorqueShift that is. My current fifth wheel is a 32' AutoMate. The GCVW is 20,140 wet and ready for the road. Rear truck axle is carrying 6240 lbs, front truck axle is 4460lbs, trailer wheels carry 9440 lbs. MT the front carries 4400,( yep that is correct) and the rear 3160. The F350 carries a tire size of LT265/75R16 with a carrying capacity of 3415 lbs at 80psi I think the F250 tires are Lt 235/65R16 with a carrying capacity of about 3100 lbs at 80 psi but double check this. I pulled that out of memory and that may not be correct but if it is I would be overloading the rear tires on an F250. Would it hurt? That decision is up to you.
I will order the 4.10 rear end. The 6.0 reaches the top of its torque curve about 2000 rpm which is 70 mph with my truck. That is too fast to tow in CA with our laws and traffic. 4.10s will bring 55 mph rpm to about 1600 in and 62 mph cruise to about 1775. Not a bad compromise. The new dually will rarely move without towing something which should be a prime consideration in the choice of your truck. If you do go with a single rear a super cab with an 8' bed will be a more stable choice for towing because of the longer wheelbase. Also a 6' bed gets really crowded with an extra gas tank, I found the stock 29 gal tank too small, the hitch. I found a porkchop tool box to go over the fender well to give some storage but it is limited.