Well, you can think of using the Due for anything where the Uno does not have enough program space, data space, or pins. You could have used an 8-bit Arduino MEGA instead, but the MEGA is more expensive than the Due...Here's a little table: Cost IOS Flash Ram SpeedUno $30 19 32k 2k 16MHzMEGA $60 70 256k 8k 16MHzDue $50 70 512k 96k 84MhzThe Due may also have a full-sized 64/80bit floating point type, which could be handy for some people.And a real D-A converter.Since it's CHEAPER than the closest equiv 8-bit system, the real question is "are there any applications that are unsuitable for a 32bit arduino?" (one that pops up pretty quick is "things requiring 5V IO.)
However, there is still one area which Atmega2560 wins Due despite its higher price. It is lower power consumption.
Running at higher clock speed, the Due has to suffer higher power consumption compared to its 8-bit counterpart.
I strongly believe that a 32-bit Arduino Due Is capable of controlling a spaceship visiting the moon and guide it back to Earth afterwards if programmed very well.