A quick way to reduce flying parts when using a chain or a cable is to take a half full sand bag and lay it over the middle. If the chain breaks it'll cause the long length to head to ground. I also have used an old fire hose and threaded the chain through that, My dad would only use a chain but put it in a pipe first but that's to awkward to carry.
I've used chains ropes and straps and only had one rope fail but we were trying to snatch something bigger than the rope's rating. Mooring lines are great, woven and braided are best, but watch the materials, polypropylene has very little stretch, and ropes really hate grease and oil. Most people don't think about it but you can wash ropes and straps, mild soap, I use Boraxo, just let them air dry.
Any of them can hurt you if they fail even cables. Nothing scarier than watching a 4" towing hawser explode.