The only difference should be the fact that 64-bit version can use more than 2GB memory if needed or if many cameras are connected. After 1.2-1.3GB the 32-bit version will crash as the rest is used by .NET and other system processes.
This is because the maximum memory address in 32-bit is: 2,147,483,647
So in most case, if you have 64-bit OS then going with 64-bit version is recommended, the minus is regarding USB cameras that will work only if the manufacturer offers a 64-bit version of the driver. For newer cameras it’s usually the case but for older devices the driver was only available in 32-bit version and for this reason it may not be listed in the list of sources when running NCS-64.
Make sure to match VLC with the used 32/64-bit version of Netcam Studio.