I've been behind too many rigs that had the straps or chains going to the body you watch it go over a pothole and the suspension compresses and puts much unneccessary stress on tiedowns.  In don't like being on the roads with these vehicles you can watch it move on the trailer, kinda eerie waiting for something to come loose.  Always tie it down tight, to the axles.

 

If your vehicle has too much movement on the trailer maybe you should put blocks between the frame and body and strap it down.

Also using your winch is not ment to tie down your vehicle and with the suspension bounce will ruin your brake on the winch, yes I have seen this happen

The straps vs chain, as long as the strap or chain is used properly and of proper weight capacity there is nothing wrong with either one. I prefer straps with covers for attaching to the axles, I use 4 of 3,500 lb WORKING load rating. I only use straps because chain wears away at steel over time.