There's very little difference in performance between 32-bit and 64-bit Windows 7. You could probably measure a difference between 32-bit programs running on one vs. the other, but it certainly wouldn't be anything you could notice in normal use.
However, if you're doing the sort of work that requires more than about 3-4GB of memory or so (video editing, batch processing of Photoshop files, running a lot of heavy programs at once, etc.) then you'll certainly notice a difference between a 32-bit system that's thrashing to the page file vs. a 64-bit system that has enough RAM so that everything can be resident.
There are also some file caching benefits to having lots of RAM.
Do bit size versions or Windows 7 editions affect the performance of my computer? All I know is that 64 bit provides more RAM capability and the higher editions provide more features.
The primary difference between 64 bit Windows and 32 bit Windows is that 64 bit includes the environment necessary for native 32 bit operation as part of the install. The reverse isn't true for the x86 version of the OS. This subsystem is called "WOW64".
On an application level, there is little to no performance difference between 32 bit and 64 bit, or (perhaps more to the point of this thread) between 32 bit apps running on 64 bit Win 7 versus the same ones on 32 bit Win 7. The primary reason why this is so is because all of the the binaries run natively on the processor. The only time you have (Had!?!? - MSFT is killing IA64 support)/i] an fully Emulated environment is on an Itanium (IA64) machine. Since the binaries run natively, performance is also at "native" levels.
Having said that, there *is* a little bit of jiggery~pokery going on under the covers in the WOW64:
The reason why is - although it all the same to the processor - on the OS level, 32bit and 64 bit programs need to remain separate from each other for data/registry/etc integrity reasons. For the most part, this means majority of the (32 bit) DLLs included in 64 bit windows are the same as their standard counterparts, and 32 bit apps simply use the appropriate DLL. The exception, and the jiggery~pokery part, is to allow for some which (for example) may share memory with 64 bit components, or otherwise need to directly interact with 64 bit system components. These use a custom calling sequence instead of the standard x86 one so that Windows can perform the redirections necessary to keep the two environments separate.
The other difference is that 64-bit Windows does not support running 16-bit Windows-based applications, whereas 32 bit does. The primary reason is that handles have 32 significant bits on 64-bit Windows. Since the handles cannot be truncated and passed to 16-bit applications without loss of data, this functionality is disabled.
I would say though, you may pick up a little speed if you are using home basic, because you don't use all the aero features and what not. But then that would be the most stripped down version of windows....