At current prices the Core 2 Quad is more expensive to purchase than the i3 processor even though the Core 2 Quad uses the soon-to-be-outgoing Socket LGA775 and uses the now-outdated "Front-Side Bus" (FSB) setup and external motherboard-located memory controller. In fact, the Core 2 Quads can cost more than the most expensive i5 and some of the lower-end i7 processors. As a result, I recommend an i5-750 or a lower-end i7 rather than a Core 2 Quad if you are going to build an entirely new system with Intel components.
Speaking of the i3, it should really be compared to the higher-end of the Core 2 Duo line since the i3 has only two physical cores. The Core 2 processors and the i-series processors are not compatible with one another (physically and electrically).