There will be some benefit to using 32 bit applications on a 64 bit operating system, as the memory limits (2GB, 3GB, 4GB) disappear. So if you're struggling to fit multiple applications into a 4GB machine that problem will go away.
Not exactly true - a 32 bit application can address only 4gb of memory - the limitation does not go away when a 32bit application is run in a 64bit environment. What is true is that each 32bit application may have its own 4gb if there is enough memory available which will result in less swap file being used.