Yes, but the effective number of registers is almost tripled. On x86 you always have at least 2-3 registers used for something you cannot touch (stack, frame pointer, etc). Hence the effective number is tripled, while the actual number is doubled.
64 bits are mostly marketting gimmick when talking about x64 hardware. Only good thing is that it supports over 4 gigs of memory. x64 has triple the number of registers you can use for general purpose - that makes a big difference for code that can benefit from it. I imagine codecs would fall into ...