In some gaming benchmarks, even the Core2Duo can beat a same-clocked i3. In most others gaming benchmarks, the C2D is not very far behind. For most productivity stuff though, the i3 wins by a fair margin by being 40-60% faster. Against a Core2Quad, i3 is likely not worth the trouble in most cases.
I personally do not like upgrading to something less than 100% faster than my last PC so I ended up jumping from C2D-E8400 to i5-3470. (My original plan was to wait for Haswell but too much swapping with 8GB RAM and all my usual programs loaded finally got to me... and if I was going to re-install the OS to upgrade to Win8, might as well do it all at once.)