Intel i3 vs. Quad Core - Processors ?

i7 = 4 physical cores / 8 threads (Operating system reads 8 cores)
i5 = 4 physical cores / 4 threads (Operating system reads 4 cores)
[dual core] i5 = 2 physical cores / 4 threads (Operating system reads 4 cores) (like an i3 but faster graphics)
i3 = 2 physical cores / 4 threads (Operating system reads 4 cores)
Qxxxx series = 4 physical cores / 4 threads (Operating system reads 4 cores)
Exxxx series = 2 physical cores / 2 threads (Operating system reads 2 cores)

Physical cores are actual 'real' cores. Threads are how many ways the data is transferred. Generally the number of cores match the number of threads but Intel's new i3/i5/i7 series have different amount of threads and cores which is called Hyper threading (typically two threads per core)
The new iX series are better because they run cooler, use 32nm, better memory latency and of course, hyper threading.
Different programs use different amounts of cores so depending on what you use, the performance will be different. If you use a program with multicore then the i7 will be faster, even if it has a slower GHz because of its 4 cores plus hyper threading (8 threads total)
Personally, I would get the i3 if you don't use any hardcore programs like Adobe Suite, or something like that.
By the way, the new i3's and dual core i5's have graphics chips built in to them. The quad core i5 and i7 do not have onboard graphics.