A 64-bit computer will be quicker when operating on 64-bit words.
A 32-bit computer can of course still operate on 64-bit words and have the precision of a 64-bit machine, but it will have to make at least two 32-bits operation to equal one 64-bit op.
Now this might not be the awnser you were looking for, though it was the one you asked. Correct me if I am wrong. I get the feeling your probably interested in running applications i.e games? Well, it all depends on the makers of the application. If it was made with 64-bit performance in mind, the 64-bit machine will be better. If they built it with 32-bit machines in mind you probably wont see much of a difference.
x86 is an instruction set, i.e the architecture of a processor. So an x86 64-bit processor is just a 64-bit processor with x86 architecture.
A 32-64bit processor sounds like you are confused to me. Its either 32-bit processor or 64-bit processor. Maybe your getting confused with some processors containg more than one core i.e x2 64-bit (That is not the same meaning as x86 by the way)