The big advantage of using a 64-bit OS is that if you've got more than 3GB RAM in your pc, the 64-bit version will pick it up correctly. The 32-bit version will "see" 3.4 GB RAM max.
Just installed Fedora 12 32-bit on a dual core with 4GB RAM on Friday and got 3.4GB RAM reported by the OS.
This is not entirely true.
A 32-bit CPU can address up 4GB of RAM but any hardware devices installed that have their own memory also need to fit into the same 4GB address space. This space used by hardware devices is generally placed at the end of the address space and any RAM in this area becomes inaccessible.
My guess is that on the machine you installed it has a graphics card or other devices using up the last 600MB of address space.
Also, it may be possible to enable PAE to allow more than 4GB of RAM to be used by mapping the physical RAM in and out of the 4GB address space as necessary.