You're kind of comparing apples with oranges there.

All dual core CPU's on the market today are 64bit, I think you want to know the difference between 32bit and 64bit?

I'm not quite sure on the just how 64bit improves performance, but the numbers 32 and 64 refer to the word length that the cpu can address. At a guess, a 64bit CPU can address twice the data in a single cycle, which makes more efficient use of clock cycles, but I could be wrong.

In a nutshell, dual core is just two CPU's on the same chip. This means you can get true multiprocessing (two processes can run at the same time, rather than a single core alternating between two processes very quickly to give the illusion of multiprocessing). Obviously each core will be running multiple processes (my machine is running 72 processes atm), but having two cores greatly helps.

Hope that helped answer your question