In past years on Phoronix there has been no shortage of 32-bit vs. 64-bit Linux benchmarks. Assuming you don't have a limited amount of RAM and under memory pressure, 64-bit distributions tend to be much faster than the 32-bit versions. However, some Linux users still often wonder whether they should use the 32-bit or 64-bit version of their distribution even when on 64-bit hardware. So with that said, here's some more 32-bit vs. 64-bit benchmarks of Ubuntu 12.10 with the Linux 3.5 kernel.
Assuming your hardware is x86_64 capable (basically any modern Intel/AMD CPU) and have at least 2GB of RAM, you really should be running the 64-bit version. The 64-bit version is faster not only because of 64-bit integer support and additional registers, but x86_64 software builds can also assume SSE instructions are handled by the processor and other safe assumptions that can't be made for 32-bit CPUs. With the now defunct Adobe Flash plug-in supporting 64-bit along with OpenJDK for Java, Wine running better now on a 64-bit stack, and other previous 64-bit Linux shortcomings having been addressed, there's really no reason not to run the 64-bit Linux operating systems.
This article provides benchmarks of the x86 and x86_64 ISOs of Ubuntu 12.10 as of this week in its near-final development state; this is for both the kernel and user-space of Ubuntu Linux. There's also the recent Linux x32 initiative, but currently no Ubuntu binaries are available of that nor is it clear right now if this x32 ABI will really take off. The Linux x32 ABI targets 64-bit hardware but with a 32-bit ABI for providing a smaller memory footprint but is able to take advantage of x86_64 instructions and other functionality.