yes the synthetic rope is strong. I have Amsteel Blue 3/16" in my winch and its rated for 5400lbs where as 3/16" cable was rated for 4,200lbs. Do some searching on the net for more info.
Here is a chart from one site that gives some comparison.
http://www.masterpull.com/cpage.cfm?cpid=197
Edit: Warn has a 9000lbs rock crawling winch they call the 9.0RC, it uses synthetic rope
http://www.warn.com/truck/winches/src/9.0Rc.shtml