Not really, as far as the OS is concerned.
The OS has (almost) everything scaled up from 32 bit to 64 bit. This includes memory addresses, but also parameters to Windows API functions (things like handles). For the 32 bit code, these are all 32 bits, so some sort of translation is required. In short, the 64 bit OS needs to create a sandbox environment that looks and feels like the old 32 bit predecessor. A good sandbox will produce little overhead, while at the same time connecting up to a new, natively written API (which is then more efficient than it's predecessor). Something IBM managed to accomplish with OS/2 2.x and later, and 16 bits Windows 3.x and MS-DOS programs.
That said, the 64 bit processor is most likely more efficient than it's 32 bit predecessor/counterpart. And one would hope that both Intel and AMD have learned from Intel's mistakes from the past (Pentium Pro, Itanium), where the speed of executing the downscaled code was less than optimal. From what I've learned to date, AMD's Opterons manage this very nicely. Intel's new 64 bit Pentiums are only now just reaching the market, so very little information is available regarding this aspect.