Mint vs Roomba 780
images from manufacturer

The two robots are now from the same company – iRobot Corp. ( iRobot Acquires Evolution Robotics, Inc. which produces the Mint).
For general difference between iRobot Roomba and Mint, you can read this post; for the Roomba 780 specifically, you can also find the following difference between it and Mint:

Schedule Feature:
The roomba 780 has on-board scheduling functionality for you to preset the cleaning time whereas the Mint has no scheduling feature.

Remote Control:
The Roomba 780 includes a infrared remote control that allows the user to control the robot from across the room, whereas the Mint does not comes with such a control kit.

Price: The Roomba 780 is much more expensive than the Mint.
The price of the 780 is $599.99 whereas the Mint 4200, 5200, and 5200 with Turbo Charge Cradle are priced at $199.99, $299.99, $349.99 at irobot.com on 2013-02-11.