Macbook Pro: Two displays - two different full screen applications
At the moment this isn't possible.

You can only have one full screen application running at a time when using full screen mode, irrelevant of how many monitors you have. With Lion you could only have the full screen application on the primary display and with Mountain Lion it was changed to allow the full screen up on any of the monitors connected to your machine.

I suspect this feature might be introduced in the next version of OSX.