When you say "the tow rope broke" what do you mean exactly? Where did it break or fail? Was it in the middle? Where it crossed under the sharp edge of the bumper? Did the stitching forming the loop come out? Did it break at a hook? Or did it simply break in the middle and well away from any splices, stitching or joints?

Each of these would mean different things. If it failed where it went over a sharp edge, like the bottom edge of a bumper, then there may be nothing wrong with the tow rope. This would qualify as a user error.

I have seem a similar effect where a manufacturer used a cheap formed sheet metal hook and within a use or two the hook had already cut half way through the rope.

Failed stitching is a manufacturers defect. Even fairly high quality equipment can show this. Don't rely entirely on the name. Nobody is perfect. Always inspect closely, inch by inch, before buying.

Some people who have reason to do a lot of dragging vehicles out of holes prefer to use chains. Chains show when they are worn or have been overloaded, the links wear and/or deform. They are much more tolerant of abrasion and sharp edges. Unlike ropes, particularly nylon, if and when the chain breaks it doesn't spring back as far or as fast. It pretty much just drops with minimal spring back.

On the down side chains are heavy, subject to rust, and require both more powerful vehicles and a change in towing practice to be used effectively. With a nylon rope or tow strap you can get a running start so a small and/or weak vehicle can often shift a much larger one.

Try that with a chain and both vehicles suffer from the shock loads. Given a running start on a chain it isn't all that hard to tear off tow hooks that aren't well mounted and/or rip or distort a unibody. So using a chain you have to slowly inch along to take up the slack and then slowly add power. It takes a larger and more powerful vehicle, or winch, to get the job done.