A big difference between 32-bit processors and 64-bit processors is the number of calculations per second they can perform, which affects the speed at which they can complete tasks. 64-bit processors can come in dual core, quad core, six core, and eight core versions for home computing. Multiple cores allow for an increased number of calculations per second that can be performed, which can increase the processing power and help make a computer run faster. Software programs that require many calculations to function smoothly can operate faster and more efficiently on the multi-core 64-bit processors, for the most part.
Another big difference between 32-bit processors and 64-bit processors is the maximum amount of memory (RAM) that is supported. 32-bit computers support a maximum of 3-4GB of memory, whereas a 64-bit computer can support memory amounts over 4 GB. This feature is important for software programs used in graphic design, engineering, and video editing as these programs have to perform many calculations to render their images.
One thing to note is that 3D graphic programs and games do not benefit much, if at all, from switching to a 64-bit computer, unless the program is a 64-bit program. A 32-bit processor is adequate for any program written for a 32-bit processor. In the case of computer games, you'll get a lot more performance by upgrading the video card instead of getting a 64-bit processor.
In the end, 64-bit processors are becoming more and more commonplace in home computers. Most manufacturers build computers with 64-bit processors due to cheaper prices and because more users are now using 64-bit operating systems and programs. Computer parts retailers are offering fewer and fewer 32-bit processors and soon may not offer any at all.