The core i3 is a newer processor by intel. It runs at 2.13GHz and has hyperthreading. This means it will likely perform better at multi-tasking than a core 2 duo at a higher clock rate. The thermal design power (directly related to heat and power consuption) is 35W.
As for the core 2 duo, you failed to tell us which model you are comparing the i3 330m to. If you are comparing the core i3 330m to a similarly or slightly higher clocked core 2 duo, it would be more powerful, especially, as I mentioned before, in multi-tasking.
I believe if you are comparing the i3 330m to a core 2 duo at 2.3GHz or higher, then the core 2 duo would be the clear winner. But do not forget to take into account hyperthreading. The core 2 duo does not have this feature.
As for power, the core 2 duo is different with each model, ranging from under 10W TDP to 40W TDP. I managed to find this:
T models: 30-39 watts
P models: 25 watts
L models: 12-19 watts
U models: <11.9 watts
The core i3 330m is a newer processor. But it does not outperform last generation's mid to high end processors. If it outperforms a "core 2 duo" will depend on which model and speed of the core 2 duo. As I said before, I would get a 2.3GHz or higher core 2 duo in my notebook rather than a core i3 330m. But anything below that, get the i3 330m.
Werxen seems to be trying to make a sarcastic joke. I don't understand why though.
To answer your question in a basic kind of way, I do believe that the I3 330 would be sufficient for you. I am typing this reply on an Dell with an I3 330M and 4GB of Ram. I can download torrents, burn a CD, play music and run other simple explorer tasks such as working with files without the I3 catching a sweat. It rarely goes over the 40% mark in the Win 7 CPU meter which would indicate sufficient headroom to do more than basic things . So based on my experience it should do the job provided my idea of basic needs is in agreement with yours. Oh and it does play wow kind of ok but that would also heavily be dependant on your GPU. Cheers.