Yes, if you run your game at native resolution. With the same CPU, GPU and RAM, running the game at 1680x1050 is a lot easier than running it at 1900X1200 so the frame rate at the higher resolution will be less than at the lower resolution. You can always choose to run either computer at a lower resolution than native (like 1440x900), in which case they should be the same. Unfortunately, LCD screens look somewhat blurry when they are run at a resolution other than their native resolution so running at a lower resolution is not ideal.
I am assuming that you're running the same game with the same settings other than resolution (details all high, AA the same, etc.) on both hypothetical computers.