From what I've seen, how well a flat tow handles depends almost entirely on the steering geometry of the toad and how much slop there is in the tie rods, etc. If it wanders all over the road when you drive it, it's probably going to wander around when you tow it, too.
A minor consideration is traction. When you tow a vehicle on a trailer, you're adding the trailer's tongue weight to the back end of the tow vehicle. This gives it more traction. In a flat tow situation you'll be a bit more prone to spinning the rear wheels when you're on a slick or loose surface. On the other hand, if you're already near your rear GAWR you may not want the extra tongue weight adding to it.
1990 E-250 Sportsmobile w/ penthouse top, converted when new by SMB Texas.