There is a far greater difference between a 32 bit and a 64 bit OS than just 32 bits. The similar user interface tends to hide the fact that internally they are really quite different. So different that Microsoft did not consider it practical to design a 32 bit to 64 bit upgrade. 64 bit operating systems do not have an inherent capability to run 32 bit applications but must be designed in, and it isn't simple.
A 64 bit OS can run most 32 bit applications but there are exceptions. Be sure an important application isn't one of them. A 64 bit OS must use 64 bit drivers, no exceptions. Be sure that all of your hardware has compatible drivers. This isn't as big an issue as it once was but still needs to be considered.