The register is a small amount of storage used by the CPU where the CPU
keeps the data it needs to access the quickest in order for optimum
computer performance. The bit designation refers to the width of the
register, thus a 64-bit register can hold more data than a 32-bit
register which in turn holds more than 16-bit and 8-bit registers. The
more ample the space in the CPU's register system the more it can
handle, especially in terms of utilizing system memory. A CPU with a
32-bit register, for example, has a ceiling of 232 addresses
within the register and is thus limited to accessing 4GB of RAM. This
may have seemed like an enormous volume of RAM when they were hashing
out register sizes 40 years ago but it's a rather inconvenient limit for
modern computers.
You shouldnt see a degradation in performance installing 64bit on a 32bit machine. I'm assuming you, like many users these days (not meant with ill intent) dont bother installing manufaterer Chipset drivers anymore and thus use basically low end drivers from MS's database.
Configure your system properly with all the proper drivers. Learn what services and MS options to disable. Try not to use AERO if you dont need it and remember with the changes in Windows from the NT Kernal to Vista+ that you will always see 50% of your ram being utilitized no matter what. However dont worry about this. Most people also dont know that software runs from memory, not off your hard disk. So obviously the more memory the better but this is debatable in one perspective. Just throwing in memory is not the answer. How you throw in memory is.
For example you will get better performance from 2x 2GB sticks of RAM then 1x512 and 1 x1GB for example. Also, remember that your MOBO may only support 2GB, so research this first.
Last but not least, you can use USB keys to improve performance by utilizing for "speedburst" (in laymens terms)
I wouldnt suggest going to 64 just because, but if you have > 4GB of ram and are using software that takes advantage of 84bit architecture (rare). 32bit should, for the most part serve you fine.
What is your intended purpose including all future intended purposes?