Windows 32 (XP, Vista, & 7) install most programs in the folder "c:\Program Files"
Windows 64 (XP, Vista, & 7) install 64 bit programs in the folder "C:\Program Files" and 32 bit programs in "C:\Program Files (x86)"
Most programs update the registry and add dll files, etc to the Windows folder and therefore can not just be copied to a new PC. However there are a few programs that are very simple and they just run. If they are in "C:\Program Files" or your 32bit PC then copy them to "C:\Program Files (x86)" of the new 64 bit machine. It used to be that you could do this more often, however most new programs can not just be copied and run. You can keep most of your old programs if you upgrade from Vista 32 to Windows 7 32, but I would not recommend it, because it will be slow and troublesome. But if you purchased the program you should have the CD or DVD and installing it is always the best choice. I have used the Easy Transfer and it works fairly good, but it will not install any programs, it just copied files and settings.
Also If you have any real old programs they may be 16 bit. 16bit programs will run on a 32bit OS, but not on a 64bit OS. But very few people still use any 16bit programs.