I think the biggest factor is the load, what is it you are trying to secure?? I use both, and it just depends on the load as to which method I employ.
For Cars, ATV's I like ratcheting straps. The cars, trucks take at least a 2" wide strap and I like to use the 10,000lb models. Most of the times I will position the straps so they are low to the vehicle (use an axle strap) while having them extent out in front of the vehicle and crossing, same in the rear.
Some times the Tire bonnets are used, they go over the tires and secure directly in front of and behind the tires.
I think chains need to be used when the load is very heavy and or when the material being secured is likely to cut,rip, tear or fray the straps. If you do use chains, go with quality chain binders. The threaded ones are the best to me. If you use a normal binder, I like to secure the handle when ready to roll (a Ty-wrap works great), this way if a little slack develops the binder will not fly open. It is also necessary to make sure that what you are attaching your strap/chain too, will hold the load. This is not a job for the . 89 cent 3/8 eye ring, Properly mounted floor D-rings, E-track or stake pockets work well, as long as they are designed to handle the load you are asking of it.