It combines historical realism and attention to detail with a sense of adventure in the vein of Indiana Jones, James Bond. Medal of Honor has an amazing use of music, it makes everything so much more atmospheric, it makes you feel like you are in a movie. The levels in MoH are also more open and fun to explore while CoD ones are completely linear to the bone. Besides, a lot of set pieces have enemies blatantly respawn over and over again. In Call of Duty you have Stalingrad which is something different, but otherwise most of the levels are just the same battleground where you have to kill the enemy at the machine gun nest and then the 5 next soldiers that will take his place.
You have a mission where you are undercover in a Submarine base in Norway, then you have Omaha beach, then one where you are infiltrating on a beautiful snowy mountain village in Switzerland (or France?) and you have a silenced pistol that kills everyone in one hit a bit overpowered, but a lot of fun to use. Medal of Honor has some really great levels full of variety. The gain in realism does not quite make up for how much worse the guns feels to shoot. The shooting mechanics are old school point and shoot, while Call of Duty weapons are terribly inaccurate unless you aim down sights, where the recoil is painful.