We towed a 24ft TT for 16 years and then switched to a 38ft 5th wheel.
To be honest there really isn't much difference 90% of the time. As long as truck, hitch and TT/5th Wheel are properly setup the stability should be there.
Here's a couple of caveats based on the TT & 5th Wheel we towed:
Both trailers had "flipped" axles. I feel because both are higher off of the ground this allows side winds to have less effect. The distance between the bottom of the trailer and the road breaks the suction/pushing effect.
The trucks and hitches were purposely setup to tow each trailer. Better brakes, better cooling, heavier suspension and proper gearing all helped to provide maximum stability.
Once you have practiced towing a trailer it becomes second nature. Anytime I get a new vehicle or RV; one of the first things I do is to go to a large empty parking lot and practice. Panic stops, turns, backing, parallel parking, tight space parking, fast lane changes...etc. This way I know how the vehicle/RV will handle.
I agree having the bed of the truck is great. With the TT we had a cap (campershell) and it provided secure storage for large items. With the 5th wheel I am able to carry lots of stuff but it has to be no more than bed rail height and not something a thief would want. Typically I have a mobility scooter broke down into six parts, a 4ft folding table and two folding chairs, wood for fires and leveling, and misc. other camping needs. Plus I have a cross bed tool cabinet at the front of the bed. There is lots of room for stuff even with the 5th wheel hitch in the bed.