Others may do a better job at this, and I'm happy to be corrected, but basically, the number of "bits" refers to the data bus width. 32 bit architecture works on information 32 bits wide at a time. 64 bit architecture works on 64 bits at a time. Simply put, the 64 bit architecture can do things faster and/or with more precision. To take advantage of a 64 bit processor, you have to have an operating system, and application software which is aware of and can use it. There -can- be compatibility problems running 32 bit on a 64 bit, and -definitely- problems trying to run 64 bit on 32 bit hardware (like, it won't even install much less run).
Personally, having programmed computer hardware starting in the 70's from assembly language on DEC PDP series systems to various high level languages, my advice is to get a 64 bit OS. Even if you end up running some 32 bit software. It is the way everything is moving because it is faster and better.
With Sonar. I gave up on the 64 bit version for now. It still has some bugs (undocumented features for you "JASPRs" :) ) that make it annoying (see my thread on the Rapture plugin). That said, the 32 bit and 64 bit co-exist with no problems. The 32 bit plugins can be installed in the 32 bit Sonar directory, and 64 bit stuff in the 64 bit Sonar. I've done it, and it all works fine. At one point, I had the 32 bit and 64 bit version for version 8.0 and 8.5 installed and there was no conflict. The different versions do share some registry information it seems, but it's not really a problem. Just make sure they each scan the right Vst directories and it all should work fine. Remember, though, that the plugins will generally have different names between the 32 and 64 bit versions and you may not be able to easily use a project created in one version in the other.
David M. Ingebretsen, M.S., M.E.
Collision Forensics & Engineering, Inc.
Salt Lake City, UT www.CFandE.com