I have no experience w/ Bias ply tires, but listening to the "blowout" stories of times-gone-by, I've heard of shredded wheel-wells and siding, uncontrollable swerving, and general Dukes-of-Hazzard-flying through-the-air-just-to-land-in-a-pig-pen attics.
What's the real deal?
Bang and swerve, or like a car tire(and my brother)..heavy but predictable?
Never predicable it all depends the prevailing conditions such as road surface, curves, straight aways, vehicle design, speed, load, wind conditions, driver reaction, and others. On a trailer most of the time when you see wheel well or siding damage it is because the tread came loose first and beat the trailer up. The problem with a trailer is often you don't realize a tire is failing until something bad happens. That is why you see trailers with skids attached so that if a tire blows it will slide instead of catching on the pavement and causing it to go crazy. Any tire can fail, modern radials seem to have a better chance of continuing to roll straighter than the older designs, but if you don't notice it went flat it will shred also. The important thing is check your tires every time you get out of the vehicle. Do a walk around looking for low tires or bulges or cracks any thing that signals failure. also check hitch and safety chains plus wiring connections. When buying tires buy a tire that is rated for way more load capacity than you will ever carry it will cost very little more and will most likely run much more trouble free. Just think of it as you taking a hike with nothing to carry then taking the same hike with a 50 pound pack on your back in the hot sun. Your tires respond in the same manner, the closer the load is to its limits the quicker it wears out.