Steel is the more resilient of the two. However, anything breaks if not cared for properly. Part of the reason why you hear so many people snapping synthetic line is because they don't winch properly. The other problem is they use a hawser instead of a proper roller fairlead. And while synthetic rope might not fray with steel wires, it can still pick up debris and stick that can hurt just as bad if not worse. The other problem is that because synthetic tow line is so new, people often think of it as a miracle tow line. Its not. You still need to size it according to your application, and the go a few sizes bigger. Most experienced winchers swear by steel, but that's partly because they know what they're doing and how to do it right and safe. The biggest problem with synthetic is with abrasion, as mentioned earlier. A snag on a small branch can drastically weaken a synthetic line, while a steel cable would just snap the branch. Then you have the myth that hawser fairleads are required equipment for synthetic lines, when they're probably the most damage causing part of the system. Go with over lapping rollers and you will avoid a lot of wear and tear on the line. The last thing I would say, and this applies to both types, is don't use a roller fairlead like a pulley! It wasn't designed to act as such. If the line of your pull is more than a few degrees off the natural pull direction of your winch, use a snatch block or pulley. Ideally, you don't want your line touching anything as it unrolls from the drum except for a pulley designed for such a task. Rollers that I've seen are usually 1 or 1 1/2 inches thick, which is not nearly a large enough curve and can put extra stress on a line causing it to break. This is how steel lines get birdcaged and deformed and how synthetic lines get stretched and frayed.
I guess to sum this up, either will really work, but ONLY IF YOU KNOW WHAT YOU ARE DOING! After all, you can't fix stupid, and I'm a big believer in natural selection.