The only real advantage I've seen that G-10 (or carbon fiber) has over FRN is resistance to heat. Other than that, in my experience, FRN is just as tough and durable as G-10. Unless it gets cut, the finish on FRN really stands up, as does G-10. My carbon fiber knives have all taken scratches, much to my dismay. I think the Volcano grip, as found on the Delica and Endura 4, is more grippy, and makes more sense being directional, than any grip I've felt on any G-10, Micarta or Carbon Fiber handled knife.
The greater structural and tensile strength of G-10 and carbon fiber over FRN is just lost on a folding knife. I don't see how those advantages really come into play in the design of any kind of knife, folding or non-folding, apart from making the knife more beautiful and valuable for that reason.
Esthetically, I think G-10 looks better than FRN, and Micarta looks even better than G-10. Polished carbon fiber looks really cool, but peel-ply carbon fiber doesn't look much different than well made G-10.
For utility, I'm all about FRN, but if you're collecting knives as an investment, or you're looking for bling, carbon fiber is the way to go. For aesthetics, I'm a fan of Micarta.
When it comes down to it, they all work about the same.