Going strictly by "Numbers", the Core2Duo would be better. E8600 vs i3 540.
However, the overall system would be better with the i3 systems, since it gives you the option to upgrade to a much better i5 or i7 LGA 1156 socket CPU's and outperforms the Core2Duo in most areas.
Depends on which model you buy. As tecmo showed that the E8600 (it is the highest rated Core 2 Duo) is a bit faster than the i3 540 (highest rated i3). But in some apps the 4 threads of the i3 may come in handy and offer you a better overall computing experience.