Here’s a piece on the Teamster’s Damage When Delivered report trying to counter the move towards non-unionized car haulers for GM and Chrysler. One of the critiques mentioned was that their non-unionized rivals “take fewer safety precautions – such as using straps rather than chains – to secure cars on the rigs.”
According to this page, some cars (Mercedes, Audis, Volkswagens) are required to be hauled using tire straps rather than chains. Chains tend to be stronger, but straps can be strong enough to do the job. The key statistic to look for in a strap is the safe working load limit or SWL. The strap proper may have a higher rating, but the SWL looks at the weakest points, usually where the hoop loops through the strap.
A light SWL might not be enough to hold down a bigger vehicle in a rough spot, so having a strong strap would be a must. At least four straps or chains need to be used for proper safety, so the Teamster’s note of some folks using two straps would be a breech of safety.
However, it seems that using straps in and of itself isn’t unsafe. In fact, chains bouncing around might be more likely to damage the car in transit than straps would and if the sales point of the Teamsters is to promote a lack of car damage, this doesn’t help their cause.
Straps versus chains is an Windows-versus-Mac type of argument, with fans on both sides. The Teamsters seem to be on the chain side, but that doesn’t make the strappers bad folks.