Should I upgrade from Windows 7 Home Premium 32 Bit to Windows 7 Home Premium 64 Bit?

I have a computer with an intel core 2 DUO processor at 2.2 GHz 800 MHz FSB and 4 GB ram running Windows 7 home premium 32 bit, should I upgrade to 64 bit. I have the disc but will it work better or worse. It only sees 3.2 GH of my ram. The graphics are NVIDIA Geforce 8200M-G? I think that is the graphics, it is integrated.