I am going to go out on a limb here and just based on your wording, I would bet that the application itself, while stating that it supports to be run under a 64bit OS, still is a 32bit application and probably one that isn't tuned to take advantage of threading it's processes to the multiple cores. Your slight performance inprovement your seeing is probably based purely on the OS being able to address more memory, thus giving your application more addressable space since the 32bit OS use to use some of that space. Also, the same statement for the processing, since the OS can utilize the multiple cores, there is more processing resource for the application to use than what is had before.
I would check to see if your application is truly 64bit itself and if can take advantage of multiple cores. My first guess is that it is not.