The main difference was that, due to Conrad's age and girth, Cannon's fistfights with the bad guys didn't last as long (or damage as much furniture) as Mannix's 'brawls of the week'. 'Cannon' made up for it with car chases, and 'trading paint' with the baddies often trying to force him off winding mountain roads.
The show would sometimes make fun of his girth. I recall one scene where he was chasing somebody in a firehouse - tried to slide down the pole, and got stuck. I also recall an interview with Conrad in which he complained about that Lincoln Mark IV they made Cannon drive. It was enormous, but low slung, and he tended to hit his head getting in hurriedly for the chase sequences.