The two Amazon links you posted are not for the same winch. As per the Rugged Ridge website,
15100.31 is the 8,500lb Spartacus with synthetic, and
15100.30 is the same winch with cable.
15100.01 is a different model entirely.
All of that is nether here, nor there. My comments were about winches in general, as my first unit was a superwinch with cable that I had planned to upgrade to synthetic. However upon researching, I came across that same warning in the owner's manual I relayed previously - winches with an internal brake can produce heat sufficient to melt synthetic line. So I do speak with some degree of experience.
@op: I'm not saying don't upgrade a cable to synthetic, just do your research with your specific model and maybe even talk to the manufacturer, rather than listening to a bunch of *******s preaching on an internet chat.