For the most part, I really never worry about the word size (32 or 64 bit) when dealing with Oracle. If you have a 32-bit operating system, then you are constrained to a 32-bit Oracle version. If you are running a 64-bit OS, then you can run either Oracle word version, but in most cases, one would choose the 64-bit version. The 64-bit version will let you allocate a larger SGA than the 32-bit version, but other than that, most Oracle DBAs never give this much thought. There are probably a few minor points to consider for a very specific situation, but I haven't run into them.
This was first published in March 2008