It runs "faster" only if the applications you are running use more than 3-4GB of Ram AND if your system has more than 4GB of physical Ram installed.
So in all likelihood it won't run mail, Safari, iTunes, TextEdit faster as they probably won't ever use more than 3-4GB of Ram.
If you are running something along the likes of Maya, Photoshop and Logic Pro and are doing something particularly resource intensive, having a 64bit system (hardware and software) with plenty of Ram won't slow down the machine when the applications exceed a 3-4GB Ram footprint as the computer won't have to resort to using very slow HD based swap-files to make up for the lack of Ram storage.
The loading of programs won't really be affected all that much unless said program exceeds the 3-4GB 32-bit limit.