|A 64 bit processor does not process 2 32 bit instructions at the same time. Instruction length varies but only one is processes at a time, just as with 32 bit processors. With multiple cores more than one instruction may execute at the same time if more then one thread is ready to run. This is often not the case.|
64 bit processors do perform better, but only when running a 64 bit OS with native 64 bit applications. With some application types the gain can be substantial, with others not much at all. With 32 bit applications most advantages are lost.
The principle advantages of a 64 bit OS are a much larger virtual address space (16TB vs 4GB) and the ability to address more physical memory. Performance gains are relatively minor in comparison.