Sounds a lot like fillrate problems to be honest.

The thing is, what is your question? The FPS breaks down because you switched computers. Just because it runs on your PC at 60 FPS doesn't mean it's locked to 60 FPS on every computer ever, obviously the other one is weaker than yours in at least one point. Without knowing more, it's impossible to tell why your FPS breaks down, which is something you should find out by profiling your game.