The Wii version, as it turns out, is content-identical to the 360 and PS3 versions, for the most part. It's reasonable to expect that the relatively weaker system will have fewer enemies and simplified geometry in some parts, but in terms of storyline, basic level design, and so on, you're getting the same game across all three platforms.
There are a few more motion controls available on the Wii. Thrusting the remote outward will perform your melee attack, while twisting it to the sides will make you lean. Finally, you can switch weapons by flicking the nunchuk to the side or throw a grenade by moving it in a tossing motion. The Wii level we played was Crossroads, which featured more-typical house-to-house fighting through a ruined, bombed-out village. When we entered one doorway, we engaged in one of Call of Duty 3's scripted hand-to-hand combat sequences, which have you struggling with an enemy soldier in a cinematic fashion. When we last saw one of these minigames on the Xbox 360, we had to merely hit the right buttons at the right time to succeed, but on the Wii, you'll actually have to hold the controllers out in front of you in a facsimile of the onscreen action and struggle as instructed by the game to save your skin and take down the bad guy.