As the title suggests, what is the difference in a banchmark software that is available in x86 and x64? As an example, we can take cpu-z or attobench as these both are available in either x86/x64. I have an x64 OS and I always use the x86 versions of every benchmark software due to compatibility with other non 64-bit machines.
There are many different types of benchmarks, which test many different things in many different ways. Some of these benchmarks will be affected by utilizing the 64-bit architecture of your CPU, some will not.
Benchmarking software specifically designed to use the 64-bit architecture will be faster/better. If your benchmark tests HDD speed like Attobench you will likely see no improvement in scores because your hard drive doesn't get faster when the application accessing it is 64-bit.
On the other hand, the x86-64 architecture supports more general purpose registers, which speeds up processing in tight (small) loops. This allows some, but not all, programs to run faster, as the CPU doesn't have to fetch as much data from main memory.
In summary, it depends what exactly your benchmark software is testing. If you are testing your HDD, for example, you should see very little, if any difference. The same applies for testing RAM speed, and 3D graphics. Some other benchmarks, however, will be affected, it all depends on exactly what your benchmarking software tests and how it tests it.