I play abit of both, too. It depends where my mood takes me really, if I'm in the mood to play a "Zombies" match, then I'll go ahead & play it, as I thought the Zombies for Black Ops was pretty decent. If I'm in the mood for a Team Deathmatch then I'll go ahead & play that.
Why I enjoy playing both? - Zombies because it gets quite challnging towards the end & you, either solo or with your friends have to complete it, which I find extremely hard, yet fun at the same time.
TDM simply because I have pretty much always enjoyed playing this Game Mode, in previous Call Of Duty games, such as Modern Warfare 2. Plus, it's competing against other players around the world, which makes it more enjoyable.
However, my favourite Game Mode on Black Ops would have to be either Combat Training or Search & Destroy, simply because they are epic.