So, I've played both and enjoy both immensly, but for different reasons.  Here's a breakdown: 

SINGLE PLAYER CAMPAIGN 

Plot 

There really isn't much of a comparison here.  MoHH2 is a WWII side story.  They tried to be creative as possible, but it still comes across as derivative and predictable.  CoD4 is a completely fictional story taking place in current times.  You have no idea what is coming next.  You won't be skipping any cut scenes like you might in MoHH2.  The graphics don’t hurt in that department either ;) 

AI

Again, this is like comparing oranges to apples.  In MoHH2, your comrades are practically useless and the enemies are completely predictable. CoD4 has some pretty damn impressive AI.  Your teammates react differently depending on which location is cleared first, so you can approach certain situations a bit differently each time and achieve unique results.  Also, you can count on them to help you out if you get pinned down or flanked.  The enemies react to your current position and they do it pretty well (all things considered). It's very immersive action that will keep you on your toes and thinking.

 CONTROLS

This is where MoHH2 shines brightly.  The Wii Remote beats the pants off dual analog.  In CoD4, to compensate for the limitations of the controller, there is a semi-auto lock feature enabled.  If you have your cursor near a target and switch to "down the barrel" aiming mode, it will snap to the target.  This works well enough, but doesn't feel nearly as immersive as the Wii Remote's IR.  Also, turning is sluggish even with x-axis sensitivity set to the max. 

ONLINE

This is a matter of personal preference.  MoHH2 feels and plays more like an "arcade" game.  It reminds me a lot of Goldeneye on the N64.  The characters seem to "float" over the surface, moving slightly faster than any human can.  It takes a lot of hits to kill an enemy (unless you get headshots), so you can get into some one-on-one shootouts that can last seemingly forever.  It's an incredibly addictive online experience.  I wish there were more maps, though and the option for voice chat.  Oh, and some blood would help kick up the fun factor (I hate to admit that, but it's true). 

In CoD4 (Note: I haven't played a ton of online yet; just a few team death mathes), the movement seems to be more grounded and heavy.  It's a lot more realistic.  You can't take a lot of hits before dying, so if you walk into a trap, you're pretty much dead without warning.  One cool feature is the instant replay of your death through the eyes of your killer.  There's something unsettling about seeing yourself get shot to death.  I like it.  Also, being rewarded for killing streaks with air strikes and helicopter support is awesome.  One thing I don't like (for now) is the ranking system.  More specifically, the fact that everyone can see each other's ranks.  When you're ranked at 4 and everyone else is at 40+ it can make you feel a bit pathetic.  I haven't hooked up a Bluetooth headset yet, so I can't comment on the voice chat right now.  I'm sure it will be a love/hate feature (I’ve already heard some annoying shitheads in the lobby before the game). 

OVERALL

Both games heavily rely on online multiplayer (MoHH2 more so) and each has a completely different feel.  In my opinion, if you could use the Wii Remote in CoD4 and the hits did a bit less damage, I would be in heaven and wouldn't need to purchase another game again, ever.  

But, as it stands now, I would choose CoD4. The campaign mode is loads better and online has tons more features.

If you're a bit more casual, MoHH2 is a great game. 

I haven't actually played MoHH2, so I can't pass judgement on it.

COD4 however is a fantastic FPS. Easily the best shooter of 2007.