Hi newcomer and welcome to the Tom's hardware forum.
1- The C2D is socket 775, the i3 is socket 1156, more new means more lifetime. Win the i3.
2- The C2D is a 45nm processor, the i3 is 32nm. Win the i3.
3- The C2D have 6MB cache L2 but don't have cache L3, the i3 4MB cache L3. Win the i3.
4- The C2D E8600 is around $289.99, the i3-540 is around $139.99, for price, win the i3.
5- The C2D don't support Hyper-Threading, the i3 support that technology.
IMO, don't have sense spend money in a socket that is old, when you can build a new rig with new technology that can have a little more lifetime.