I don't find with any proof that the general operating system (Windows) itself runs any faster between 32-bit and 64-bit. However, usually 64bit systems do have a bit more RAM...so any speed increases are most likely the result of the increased RAM and not the fact that 64 bit is faster or more efficient.
Any pitfalls? For sure. Any piece of hardware that you use, both internally in the computer, as well as external perhipherals MUST have a 64-bit driver
to work. If you have no 64-bit driver, it's not going to work. As far as software goes, a 64-bit OS can run 64-bit apps and 32-bit apps. However, it cannot run 16-bit apps...so if you have any of those...they aren't going to work.
Some applications (those using large datasets), benefit greatly from 64-bit. However, you have to have a 64-bit processor, a 64-bit OS as well as a 64-bit application. These big apps consist of things like large databases (SQL Server, Exchange Server), graphics and photo editing packages (Photshop, CAD stuff, etc), and potentially media encoding applications.
Therefore, the overwhelming majority of software that most consumers use won't be any faster as you will still be using the 32bit version or it simply won't be a big enough dataset to really benefit from the 64-bit version.
Personally, I would not go from a 32bit box to a 64bit box simply to get a little more speed. I would upgrade if you were going to run native 64-bit apps or wanted to expand your RAM to 4GB or more.