Other than more support for Memory etc... The main advantage of it is that it was made specificly for 64-bit architecture.
As an FYI kinda thing, a quick explination of 32-bit VS 64-bit
Think of it like a highway, but rather than cars.. data. 32 lane highway can flow alot of traffic, but a 64 lane highway will flow twice as much, in the same ammount of time.
Now on that note, when your operating system was specificly designed for that purpose, you will take full advantage of your "bandwith" and in so doing this, gain better performance.
Aint nothing worse that having a hotrod with 800hp that wont go past 90 because of other limitations
Also, the x64 OS has the same Kernel as Windows Server 2003