The 6.7 Diesel engine trucks weigh about 600 lbs more than the 6.2 L gas, with most of that being the engine.
So, you will have a reduced payload with the diesel, in either F250 or F350 form.
My 2016 F250 4x4 shortbed crewcab gas payload is at 2749 lbs, with a 3.73 axle ratio. With the camper package, it's effectively an F350, but I can fit in in the garage since it's not as tall (only 2" blocks vs. 4" blocks)
If they wife likes a lot of amenities for full-timing, you will probably be limited to some of the lighter 5th wheels with the gas motor, even if you got the 4.3 axle ratio, which is rated to pull 15,000 lbs.
I probably would not pull over 10-11k with the gasser, if you were planning on pulling some serious mountain passes, but you can do it.
Diesel is of course more expensive, as it is an $8k+ option, and being a higher performing engine, more maintenance (people argue this, but higher specs=higher maintenance in my book).
You can't have enough truck, seems to sum up the wisdom around here. Take it for what it's worth. It's YOUR wallet. You can probably find some smoking deals on the 2016's. You're talking 9-12k off or more, if you are willing to do a little compromising. Everything in life is a compromise, more or less.