Here are some difference between iRobot Roomba 560 and 780.

Roomba 560 VS. 780
images from manufacturer

* AeroVac Technology and Brush:
The 780 features AeroVac Technology and improved brush system to dramatically reduce hair wrapped on brushes.

* Virtual Wall / Virtual Wall Lighthouses:
The Roomba 560 comes with 2 Virtual Walls, while the 780 includes 2 virtual wall lighthouses.

* Control Panel:
The 780 uses Touchpad Control while the 560 uses Buttons.

* Full Bin Indicator:
The 780 includes full bin indicator while the 560 does not.

* Debris Sensing：
The 780 features Dirt Detect Series 2 which use both acoustic and optical sensors to locate dirty spots, while the 560 features Dirt Detect which use only acoustic sensors.

* Persistent Pass Cleaning
The 780 features the Persistent Pass Cleaning which uses a back and forth cleaning pattern to clean areas where it senses dirtier.

* Control Kit
The 780 includes a remote control while the 560 does not come with.

* Bin Type:
The 780 includes the AeroVac Series 2 Bin which uses a powerful vacuum to pull debris and hair off brushes into the bin. And

it holds more than standard bin that the 560 uses.

* Filter Type:
The 780 features the Dual HEPA Air Filters (output fresher air), while the 560 use standard filters.

* Extra Brush Cleaning Kits
The 780 comes with 2 Brush Cleaning Tools while the 560 has only 1.

* Extra Brush Set
The 780 comes with 1 extra brush set including 1 extra bristle brush, 1 flexible brush, and 1 side Brush, whereas the 560 has none.

* Price:
The 780 is priced at $599.99 while the 560 price was $399.99, now $349.99 at irobot.com (on 2013-02-08).

* Weight:
The Roomba 560 weighs 8.3 pounds while the 780 weighs 8.4 pounds.

* Dimensions: the 780 is a bit larger.
The 560: 13.4 inches in diameter, 3.6 inches in height
The 780: 13.9 inches in diameter, 3.6 inches in height

* Advanced Cleaning Head
The 780 features the Advanced Cleaning Head which provides better performance for picking up pet hair, dirt, and more.

* Extended-Life Power Management
The 780 features Extended-Life Power Management which help deliver longer battery life.

* Recharge Time
The 780 recharges faster.

Similarities:
features on-board scheduling;
adjust between carpet, tile, hardwood and linoleum floors automatically;
return to home base automatically;

Do you know more difference between Roomba 780 and 560, please share it below, thank you.