Interesting. Perhaps the current milliseconds returned from the System class might vary? This part is still a mystery on why it's movement vary from one computer to another.
Keep in mind that unless you use interpolation the visual of movement may vary wildly between computers. For example even if you use a delta to move 10 meters in your game every second, one machine may loop 120 times a second, thus incrementing your visible position slightly each frame, the other may loop 40 times a second and although you will reach the same position, the movement will appear completely different.
Then again I'm not sure what you mean about the movement varying, is it just a visual difference or is it actually moving farther? If you multiply your movement by time it should be consistant between systems.
Also, you're citing the only difference as that the desktop is 64 bit while the laptop is 32, but it sounds to me like they probably vary a lot in performance and hardware as well.