Er, 64bit has nothing to do with the number of cores. 64bit is how much data a processor holds in it's data and address registers. It means faster processing for large numbers, and easier access to large memory addresses.
In reality, the big benefit of 64bit architecture is the fact that you can have way more than 4gb total memory in your computer.
32bit OSes do infact use both cores. In fact, 32bit OSes are usually faster for running software that's compiled in 32bit mode due to processor emulation. 64bit apps running on 64bit processes should theoretically be just as fast though.
And the speed difference is marginal though on 64bit OSes running 32 bit softare, because of the fact that you can use more than 4gb of ram.