I went with synthetic when I put a winch on my TJ - mostly for a little weight saving on the front end and also because the fair lead for synthetic has a cleaner look than the roller lead. I used it a couple times myself with no issues. Very easy to handle & spools easily and smoothly if you guide it. However, my son used it once to get a friend unstuck - needless to say, he wasn't as careful as me & the rope got chafed & pinched in a couple spots. Now I'm not sure I'd trust it anywhere near the rated strength but haven't had a chance to replace it. If I had it to do over I'd do steel wire rope for peace of mind.
Another poster said it best "how many wreckers & commercial rigs do you see running synthetics?"
If you do go synthetic, make sure to keep a cover on the winch to protect from sun & road debris.