It plays very similarly to MW, almost identical but the guns do make you play a little bit differently than MW, not much though to be honest. A lot of the maps are huge and the Nazi Zombie mode is better than it sounds, but only with friends. If you like WW2 shooters then you should buy it because you'll definitely enjoy it. Especially if you enjoyed MW. In my opinion Treyarch made a mess of COD3 when compared to COD2. But they definitely improved on, and made a better game than MW, with WAW. I actually prefer WAW to MW2.
The single player is very good and if you decide to take up the Veteran challenge make sure there's nothing in the vicinity that can be broken. I was so tempted to just throw my controller across the room but it's not his fault that the game was so damn hard on Veteran! This thread is making me want to go and buy it on PS3 after the sale of my 360.