x64 is actually slower then x32 bit because of some background code and overhead but you won't notice the difference. It is only a percent or 3. You also can use higher amounts of ram depending on the OS version you purchase and the limits Microsoft puts on their versions.
Long story short, a 32-bit OS can only read 32-bits of data at one time. As a result, there is a hard limit of 4GB the system as a whole can access. [The amount usuable by you is less then that; usually around 3.25GB or so after hardware gets mapped. The amount usuable by a single program is only 2GB].
A 64-bit OS can use significantly more RAM, though the OS usually limits the total amount to something easier to manage [192GB for Win7 professional]. Another major change is that even 32-bit programs can access up to 4GB of RAM themselves, double what they could under a 32-bit OS [assuming they are compiled as LAA at least...]. So a memory intensive 32-bit application could see a significant speedup under Win64, though this is a rare case.
There are plenty of other under the hood changes, but to you, the increased RAM is the primary reason to go with a 64-bit OS. There is very, very little reason to bother with Windows 32-bit at this point.