I often get asked this question 32 or 64-Bit? In the past I have told people to stick to 32-Bit because of compatibility issues but things have changed now. Quoting for Phoronix which recently did a benchmark test between 32-Bit and 64-Bit.

Going back years we have run 32-bit vs. 64-bit Linux benchmarks. While the results seldom change, we keep running them as the question of choosing between a 32-bit and 64-bit Linux distribution image is still a popular question… These tests drive in a surprising amount of traffic and I continue to be flabbergasted by the number of people still asking this question when nearly all modern x86 Intel/AMD hardware fully supports x86_64 and it generally means much better performance. Usually the only caveat in not using a 64-bit Linux image is if running a system with less than 2GB of RAM.

In the past there were issues surrounding the Java and Flash support for 64-bit Linux along with an assortment of other possible problems (e.g. with Wine), but all those major issues are a matter of the past. 64-bit Linux is in great shape and as long as you have a decent amount of RAM you really should be running 64-bit Linux.

If you are still in doubt, read the full article for the benchmark results.