I think epoxy resins are more common with Carbon Fiber, at least that is what was used in the sailplanes and Thunder Mustangs I have worked on.
But then Polyester resins mostly aren't used even in fiberglass for the sailplanes.
I recall epoxy burns pretty well, but maybe not quite as well as polyester.
I do have a small piece the the prototype Thunder Mustang that crashed (is the piece of the gear door that had my last name as part of the crew on it) it burned all around most of my name but my name is still on it not sure why it didn't burn the whole thing. I suspect the resin we used required a bit help to maintain the flame. But then there was the other Thunder Mustang that was destroyed in Reno when the brakes caught the sage brush it stopped in on fire.
Brian
CFIIG/ASEL