We pulled a 36' 5er for 10 years before getting the MH. We loved it! I never owned a TT, but I've heard some horror stories about fishtailing, etc. Our 5th wheel was steady as a rock at any speed, although we tried to keep it at no more than 60 MPH for safety. We pulled it with a Ford F250 PSD SRW, not a dually, and never had a problem.
Good luck, happy trails, and God bless!