First of all, they don't make many "small" fifth wheel RVs. The smallest has a GVWR of about 8,000 pounds.
The difference in an 8,000 pound TT and an 8,000 pound 5er is hitch weight. Estimate the TT hitch weight at 12 percent of trailer weight, but estimate hitch weight of a 5er as 17 percent of trailer weight. So for an 8,000 pound trailer, TT hitch weight will be about 960 pounds and 5er hitch weight will be about 1360 pounds. Very few F-150s can tow an 8,000 pound TT without being overloaded, so an 8,000 pound 5er should be out of the question.
For an F-250, it depends. Before 2005 model year they had only 8,800 pounds GVWR. My '99.5 F-250 CrewCab diesel 4x2 was overloaded with an 8,000-pound 5er. Beginning with 2005 model year, they had 10,000 pounds GVWR. So a 2005-up F-250 can handle an 8,000-pound 5er without being overloaded. But not much more than an 8,000-pound 5er. If the trailer you can't live without has a GVWR of 10,000 pounds to about 12,000 pounds, then you need an F-350 with single rear wheels (SRW) to tow it without being overloaded.
5ers don't beat up the truck any more than a TT, but it's much easier to overload the tow vehicle with a 5er because of the increased hitch weight.
For a TT, definitely. Almost all knowledgable RV folks say you need a weight distributing and sway controlling hitch for any trailer that weighs more than about 5,000 pounds. And many lower that to 3,500 pounds.
There are two basic choices. Ordinary WD hitches with sway control that cost less than $1,000, and the really good ones that eliminate sway for over $2,000.
Right now I have one of the cheap ones that works good as long as I don't get into extreme conditions. It's a Reese Strait-Line dual-cam.
Strait-Line Weight Distribution with Sway Control - Trunnion Bar - 10,000 lbs GTW, 800 lbs TW Reese Weight Distribution RP66073
When shopping for a WD hitch, ignore the GTW rating and get enough hitch weight capacity to handle 15% of your trailers GVWR. IOW, if your hitch weight could exceed 800 pounds, then don't buy a hitch with a max hitch weight capacity of 800 pounds.
My hitch is left over from use on my cargo trailer, for which 800 pounds max hitch weight was appropriate. But for my new TT, hitch weight could be a bit over 800 pounds when loaded for bear. So I'm saving for a ProPride that costs over $2,000. It's the best on the market right now.
Trailer Sway Control Hitch Guaranteed to Eliminate Trailer Sway - ProPride 3P