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What unit do you have? My 30' 16.2GVWR 5th has a 3300lb loaded pin so I'm interested in who makes a 44' that is so light.
It in my sig line. XLR 395AMP. It certainly isn't light though and can go over 20k when the garage is full and there is water in the fresh tanks. It just has a lighter pin weight due to axle placement.
An SRW 350 is very capable and is a good option. It will never be as stable as a DRW though. I tow a variety of TT's and 5ers and the comfort and security of the DRW is significant.
If you decide to go DRW, then you need to decide between 350 and 450. The 350 offers more cargo carrying capacity, but the 450 has bigger brakes, wheels, differential, and frame. The 450 also has a tighter turning radius, though I must say I really haven't felt limited by the turning radius of my 350.
The larger diameter tires of the 450 effectively reduce the drive ratio, so it may actually get better fuel mileage than the 350, though this is just speculation on my part.
When both the SRW and DRW are rated to do the job, it's up to you to decide what your priorities are. Asking what others would do is just going to get you a lot of differing opinions. There is no right or wrong. Only different. Kind of like pizza toppings or ice cream flavor...
For the sake of discussion, let's say GVWR 20,000, Hitch Weight 2,800. Grand Design 381M.
There are so many variables that it is best if you compare hard numbers -
check out the Ford towing guide - specifically pages 25 and 26 - though there is a wealth of information throughout the document.
IMO, with a 5th wheel that big, go DRW. I daily drive my F450 and enjoy the experience. When I tow, there are conditions where I'll be OK with my DRW, and I likely wouldn't be OK with a SRW (e.g. losing a rear tire on a turn, needing to swerve near the truck's limits...)
Also, consider how much weight you have in the truck. With my family of 5, hitch, dog, firewood, etc. I'm over 1000# plus my pin - this puts me over the F350 SRW 4x4 6.7.