Chains are the more secure of the two. The chains are attached to mounting points on the frame of the car and then tightened. Some cars have these mounting points and others don’t. Chains sometimes get a bad rap, if used incorrectly they can cause serious damage. But this is car carrier 101, chances are the people who’ve had a bad experience with them aren’t professionals. NEVER loop the chain around suspension or drivetrain components.
Wheel straps are straps that go on your wheels. Ratchet straps to be specific. This method is used if the car is sitting on a certain part of the trailer that a chain can’t get to or if the car will scrape if it gets any lower. Sports cars and custom lowered cars require these all around to prevent and damage to the bottom of the car.
What is safer?
Straps are usually better for the car but chains are more secure.