I think it depends on how robust your trailer body and its contents are and where you intend to take it. I'm looking at using composite panels with little or no framing for my next build and I have no doubt that independent suspension will be "kinder" to the body. Check out the Track Trailer vid. Pretty amazing viewing.
The difference between the truck and trailer in that video is not because of the difference between independent and solid beam axle suspension. Well... it is in a way, but not for the reason you think.
The difference you are seeing is because the trailer's suspension has a much lower unsprung mass. Not because the trailer's suspension is independent. The independent suspension has a lower unsprung mass.
I also fail to see the point in putting a more sophisticated suspension on the trailer than what is on the tow vehicle. So the trailer is capable of a speed which the tow vehicle is nearly uncontrollable. Slow down, before you crash.
A couple other points:
1) An independent suspension with 35" tires has huge unsprung mass, and you loose that benefit anyway.
2) a trailer live axle will have less unsprung mass than a truck axle anyway, since there is no driveline inside.
Sean touched on the other reason why I think independent suspensions are not necessary. A trailer is a tripod. No matter WHAT you do, independent suspension with airbags, etc... the trailer is a tripod and it will always tilt when one side goes over an obstacle. Articulation is meaningless. That trailer could have air bags, linked airbags, springs from a Nissan Micra, it doesn't matter. It will tip.
At speed, you can get some independent action, however. The inertia of the trailer stops it from tilting, so you need to be able to absorb bumps on one side. However, solid axles can and do absorb bumps on one side. The only negative aspect, is that the other side experiences a camber change when one wheel hits a bump.
That's bad for a sports car. I don't see why a trailer would care. If it really makes a difference, you're probably cornering way too fast on a bumpy road, and as the video demonstates, the truck probably already lost control as well.