I notice that Leon uses comparatively more leg-based fighting than Chris, who comparatively uses more upper body strength. In Leon's fight with Svetlana, he uses an elbow, a spinning kick, followed by two knees in a row. Leon's most common melee in RE4 was the roundhouse kick, while Chris' most common melee in RE5 was the haymaker punch. In RE6, their coming from behind melees are strikingly different too; Chris has a neck break, using sheer arm strength, and Leon has a flying move that slams the enemies' head into the ground, relying on momentum. Leon's headshot frontal melee also relies on momentum, flipping the enemy over his back and on to the ground.
This leads me to believe that Chris relies more on boxing (due to all his punches,)/wrestling/military hand-to-hand (due to his neck-breaking), while Leon relies more on Jiujitsu (due to his momentum based head shot melees in RE6), Tae Kwon Do (due to his frequent kicks in the games), and Mui Thai (outlined by his use of elbows and knees in the Svetlana fight).