the software has to be native x64 code to see improvements and it's only a 10-15% improvement. otherwise, it just let's you use more of your RAM. With x86 (32-bit), you're limited to 4GB of address space. that means a TOTAL of 4 GB for everything you own. That means if you have a 1 GB graphics card and 4 GB of RAM, you'll only see 3 GB of RAM because 32-bit can only recognize 4 GB total. There are ways around the 32-bit limitation (read: PAE) but it's just easier and better to go to a 64-bit OS.
then you factor how software factors into this address space and 32-bit because a real problem. On 32-bit Windows, in normal configurations, each program only has a usable address space of about 2GB, half of the total memory that can be addressed with 32-bit addresses. This means that the amount of RAM that the program can manipulate directly is limited to 2GB. If the program needs to work on a larger chunk of data, it has to move that data in and out of RAM a piece at a time, usually storing it on disk when it's not in RAM. This 2GB limit is regardless of the amount of physical memory installed; if you run multiple programs, they each get a 2GB block of their own, so they can use many gigabytes in total, but any individual program can't readily break through this limit.
another thing is 64-bit code is more secure. there's malicious code that's designed to fill up the address space and execute. that's many times easier to fill up the space of a 32-bit system due to the very very small address space. unfortunately, as long as you're running 32-bit software on your system, as long as the exploit can take advantage of that particular software, you have a vulnerability there. but it's a 1-to-1 exploit. so if some malware guy writes something to target 32-bit Adobe Acrobat Reader but you don't have that program, it doesn't matter.
most software is still 32-bit, including most TV software. If you move on to more complicated software like video editors, many of them like Adobe Premiere ONLY have a 64-bit version.
there's really no point in installing a 32-bit OS at this point, especially since the 64-bit version can run 32-bit software. the only time you need a 32-bit OS is if there's a particular hardware device you own that has no driver in the 64-bit OS and it's such a legacy device that the company has not made a driver for it. that said, a lot of old devices still have drivers that'll work.