The frame rate should be the same from computer to computer, but only if the computer is fast enough to display it at the intended frame rate. If the frame rate is set at, say, 120 fps (way too high!) and the computer only has enough resources to show 30 fps, it's going to take a lot longer to get through the same number of frames, and the animation will look slower. It's all in the way the avvie was set up originally, and in how much brainpower the compy can access how fast.
That's if it's doing it consistently, of course. Every once in a while, my compy gets bored and decides to speed things up, but a refresh usually cures that.