welcome to the forum.....
The F250 sure won't have any issues at all pulling or carrying 1800-2000 lb hitch weight from a 260RD Reflections 9500 GVWR 5th wheel trailer. The 6.2 engine is a good match up with that size trailer.
Your pulling a trailer much heavier than your old one so you will notice the weight difference. I've pulled several of both (rv and non rv) and found the 5er more stable going down the road in all conditions.
Someone says get G load range tires (4080-4400 lb capacity per tire). Thats not a good idea on a trailer that small with approx 2500 lb per tire load requirements. Kinda' like putting 22.5" semi truck tires on a 1/2 ton truck.
Enjoy the 260RD trailer.
