Off-road tires do give you better puncture resistance when taking a trailer to places that have sharp rocks; I know that for a fact. Went through three ST tires before swapping out to AT tires and never had a flat. But I also have a large popup that is designed to take off-road and I don't mean gravel roads.
HOWEVER, my trailer came with 175/80-13 tires. The trailer was lifted to add about five inches of clearance, and the dealer put on 205/75-14 ST tires; these were the tires I kept destroying.
I installed 215/70-15 AT tires, but I had plenty of room and had to replace all the rims, including the spare.
But replacing a ST tire with the same size AT or MT tire is hard to do and keep the same load capacity. ST tires do have a great load capacity per size than any tires I could find.
My 175/80-13 (original for the trailer) were rated at 1360 lbs, the 205/75-14 were rated at 1760 (quite a bit higher than stock), the 215/70-15 tires I ended up with are rated at 1653 lbs. Still 293 lbs over stock.
And since the axle remained the same, the larger tires DO NOT increase my load capacity of the trailer. But except for water and a duffel bag full of clothes, I tow with the trailer a good 400 lbs below maximum weight carrying for the trailer.
As for highway towing, I feel no difference. Some say the ST tires track better, if the did, I can't tell a difference between the two. And after thousands of miles, they are wearing nice and even.
Trailer: Lifted 228BH, heavy duty springs and Yokohama tires
TV: 2016 GMC Sierra Z71 4x4 CC, SLT
Spare TV: Two Alaskan Malamutes
Living somewhere in ID; previously lived in Moab UT; previous to that, don't ask!