"Any CPU" will generate MSIL that can JIT to either environment, but take no advantage of either. x86 and x64 force that environment [and x86 will run on an x64 platform, but as a 32 bit application.

Just remember that (in general) x64 means bigger and slower applications.

What you GAIN is a larger virtual address space. If your machine has <=4GB of RAM, you are likely to see an overall performance decrease. The same applies if your "typical running condition" is under 3GB total virtual address space.

The benefits (again, typically) start to appear when you have 8GB-64GB (or more) on RAM on your machine.