Maximized window on both displays on OS X 10.8.3
UPDATE 2

These are the support instructions for using multiple monitors with Mac OS X 10.8 (Mountain Lion) and earlier. You will likely want to use the Extended Desktop Settings. If you still doesn't let you see the other app, then check to see if FCP has an Always On Top setting which may be turned off, and don't have the apps set to full-screen mode.

UPDATE

This solution will only work if you are running Mac OS X 10.9 (Mavericks) or later. (Apologies as I missed in your question that 10.8 was Mountain Lion and not Mavericks).



If you do find it, then set that. Then go to one Desktop and Ctrl + Click on the FCP icon in the Dock and under Options, select This Desktop.

Then go to another desktop, Ctrl + Click on the other apps icon and under options select This Desktop.

Then you should be able to go to one monitor and select the FCP Desktop, move to the second monitor and select the other Apps Desktop and that should display both apps on the respective monitors.

This is Apple's support page for Multiple Displays.