Performance-wise, the Core Duo will beat the Atom, probably by a long way, but the Atom uses much less power and should have a significantly greater battery life.
So really it depends on which you prefer: a cheap system with a longer battery life which will be fine for web-browsing and the like but won't be much good for games or video editing or whatever, or a more expensive system with a shorter battery life which will handle more CPU-intensive tasks.
C2D will be my choice, even over battery life to be fair, have used an atom laptop and its ok unless you try do more than one thing at a time, really slow, hence XP still being the os for it...
Core2Duo over Atom anyday, Unless you have some strange desire to use 64bit Addressing, which the Atom can do despite being only a 32bit.. However I have an Atom one of the first ones and I have to say it can hold it's own against my P4 2.6. However that may be the ram making the difference....
I'd probably go with the core duo, since it's dual core, whereas most Atoms are not. Ulysses35 is right about the atom though. I recently got a Netbook, and as long as I'm not doing anything it works great but as soon as I start to do things (like open iTunes), the performance just goes to crap. If this is going to be your primary computer, I strongly suggest the core duo.