I beg to differ with Maz - I've been running 64 for half the year now and haven't found any recent 32 bit apps/games that aren't fully functional. It runs everything I've put on it, full stop. So IMHO, it is overblown at this point to spend a lot of time belaboring compatible or non-compatible software.
I'm not bringing this up as an
OhMaiGawdz h0w darez he di$s tha 64-Bitshizzlez, but simply to point out that the compatibility stuff os overblown, and there are valid reasons for a home enthusiast to use V64.
As to 'What's the Difference' - In simple english, 64 bit operating systems read/use instructions which are twice as long, and have addressable space which (theroretically) can handle 16 Exibytes of addressable space
(two bits times 10 to the 64'th power). Something like 10 million times what a 32 bit OS can handle. Why is that important now?? Because 32 bit windows can "only" handle 4 GB of addressable space, a good chunk of which is needed for devices and communications - This is why people with 32 bit OS's cannot utilize 4GB of RAM, and the is the primary reason why enthusiasts are beginning to switch to 64 bit.
Vista 64 has the libraries needed to run 32 bit code. 32 bit applications run using the included set of DLL's (libraries) to do the work of translating between the two. There is obviously going to be some performance overhead, since you're running your 32 bit apps inside what amounts to a container/translation layer.
But many of the common commands which are less than 32 bits in total length can be grouped to run in pairs as a single instruction. The rule being that there has to be enough space within a 64 bit command for both 32 bit instructions plus the necessary tags needed to differentiate the two. Actual performance will obviously vary depending on exactly what you are doing, but to a great extent the added efficiency of grouping instructions offsets the performance penalty of having to run a translation layer.
In practice, I haven't noticed any difference. Apps, games, whatever.
Also - let me ask a question: Set aside the 32 or 64 bit thing for now. Do you normally use 3rd party apps for music and video??? And do you plan on contunuing to use these on your new comp??? Of the answer to these is
"Yes, I use 3rd party apps for music and video, and intend on continuing to do so", then I would suggest you look into using the Business version instead of Home. Home's selling point is the 'free' Media Center/Movie Maker apps for music and video which are included with the OS. But if you're going to replace that anyhow, then there's no point. Better to go with Business for the security upgrades and superior Backup and Restore functionality
(You get Windows Fax and Remote Desktop as well, but I don't see many home users playing with these...).
Wiki:
http://en.wikipedia.org/wiki/64-bit
M$FT:
http://windowshelp.microsoft.com/Windows/en-US/Help/41531554-d5ef-4f2c-8fb9-149bdc5c8a701033.mspx