Carbon flexes less, making it more prone to cracking on hard impacts. I believe glass is more forgiving (more flex), but is definitely heavier. I don't know much about Kevlar.
For surf, it seems that a carbon/glass combo hull is best to combine weight loss and strength. Or full glass if weight isn't an issue (for big surf).
Full carbon is pretty much flatwater only. I'm sort of guessing that Kevlar acts as a middle ground between the two, but I'm not sure.
Hopefully a more knowledgeable person will clarify. I run a carbon/glass hull.