AutoCAD versions since AutoCAD 2008 (and since AutoCAD LT 2009) have included both 32 bit and 64 bit flavors on the same media. If you install on a 64 bit Windows system, you get the 64 bit AutoCAD; otherwise you get the 32 bit AutoCAD. The 64 bit AutoCAD can take advantage of as much memory as you can throw at it, whereas the 32 bit version is limited to 2 GB (3 GB if you cheat). They should be otherwise identical in theory, but in practice there are major differences.
One big difference is VBA. Microsoft put VBA out to pasture many years ago when they introduced the .NET framework, so there will never be a 64 bit version of VBA. Autodesk had to resort to a seriously inefficient kludge to get it to work at all in the 64 bit flavor of AutoCAD (VBA has to run in a separate 32 bit process, which makes typical applications two orders of magnitude slower).
The other big difference is that any third party ObjectARX applications must be installed for the correct architecture. A 32 bit ObjectARX application will not work in a 64 bit AutoCAD. [Note that .NET (or "managed") applications typically work fine in both architectures -- I'm referring to native C++ ObjectARX applications only.]
On the Autodesk discussion groups, many people ask how they can install the 32 bit version of AutoCAD on their new 64 bit operating system. Why would they want to do that? Almost always because they need to use an application that is only available for 32 bit AutoCAD architectures, or because they discover that their VBA applications become unbearably slow.
It is possible, with some hacking of the AutoCAD installation database, to install the 32 bit flavor of AutoCAD on a 64 bit system, but I don’t recommend that. There is just no excuse any more to not support the 64 bit architecture. If you find yourself in this situation, put pressure on the developer of the application to get it ported.
In fact, if you rely on an application that hasn’t been ported to the 64 bit architecture, I’d like to hear from you. Add a comment to this post and let me know the name of the application. If you are a vendor or developer that has not yet ported your 32 bit application, please contact me — I will gladly port it for you. Even large applications can typically be ported in several hours.
BTW, I am well aware that even Autodesk is guilty of not supporting 64 bit platforms in some of its vertical market AutoCAD versions (and corresponding object enablers). I certainly hope they remedy that situation in the next release cycle.