Full blasters/weapons fighting (strength, dex, and con) Canderous has the experience and grit of a ground trooper. He's been around and lives for the wild fights. I'd give the win to Canderous. Carth might get out of tight situations, but Canderous seems intelligent enough not to easily lose an escape artist (intelligence).
Ship vs. Ship. (intelligence and Charisma/leadership) Carth would probably pull off a win in both a single pilot figher (add dexterity) and a cruiser, though it wounds like Canderous isn't a slouch in that area either.
Ground army vs. ground army. (Intelligence and Charisma/Leadership) Probably Canderous. As far as I know, Carth probably has little experience here.
Ship fleet vs. ship fleet. (Intelligence and Charisma/Leadership). Hmmm, tough one. Either of them have high level officer experience? Did Carth co-command a fleet?