Roomba 660 vs 650
images from manufacturer

Seems they are the same robot except for the color and the accessories they include.

* Color:
From the above pictures, you can see that the 650 is black, while the 660 is olive.

* Accessories:
The Roomba 660 comes with more additional accessories.
The 650 only comes with 1 extra AeroVac filter (the product description on some online stores state the 650 also comes with brush cleaning tool, but some do not say it has the brush cleaning tool), whereas the Roomba 660 comes with 4 extra AeroVac filters, 1 extra bristle brush, 1 extra beater brush, 2 additional side brushes, and brush cleaning tool.

Otherwise, they are the same.

They both come with Virtual Wall, but does not includes the Lighthouse;
carry 1-Year limited warranty on Robot, and 6-month limited warranty on battery;
feature 3-stage cleaning system and iAdapt Responsive Cleaning Technology;
have onboard scheduling functionality that you can set it to run automatically up to 7 times per week;
features the Dirt Detect Technology to locate dirtier spots;
return to the home base automatically to dock and recharge;
automatically adjust between different types of floor surfaces;
include Soft-Touch Bumper;
include cliff detection sensors to avoid drop-offs.

If you know other difference between Roomba 660 and 650, please share below.

Roomba 660 vs 780
images from manufacturer

Price:
The Roomba 660 is cheaper than the 780.

Control Panel:
Roomba 780 includes Touchpad controls while the 660 uses buttons.

Virtual Wall vs. Virtual Wall Lighthouses:
Roomba 660 comes with 1 auto Virtual Wall whereas the Roomba 780 includes 2 Virtual Wall Lighthouses.
The virtual wall lighthouse has a ability to navigate the Roomba from room to room while the virtual wall doesn’t have.

Control Kit:
The Roomba 780 comes with an infrared remote control which lets user to control Roomba around the room, whereas the 660 doesn’t comes with the romote control.

Bin Type:
The Roomba 780 includes AeroVac Series 2 bin while Roomba 660 includes AeroVac bin.

Full Bin Indicator:
The Roomba 660 does not comes with a full bin indicator which the Roomba 780 includes.

Filter:
Roomba 660 uses AeroVac filter whereas the 780 features Dual HEPA filters to capture tiny particles and output fresher air.

Dirt Sensing:
The 660 features the Dirt Detect Technology while the 780 features Dirt Detect Series 2 to locate dirtier spots.

Persistent Pass Cleaning Pattern:
Roomba 780 includes the Persistent Pass Cleaning which uses a back-and-forth cleaning motion to clean dirty spots whereas the 660 doesn’t feature this.

Performance:
iRobot claim that the 780 pick up mess better than the 660.

Simlarities:
• Include iAdapt Responsive Cleaning Technology to clean your home thoroughly.
• Both have on-board scheduling that lets you schedule them to vacuum whenever you want them to run.
• Return to the home base automatically to dock and recharge.
• Automatically adjust between different floor surfaces.
• Include Soft-Touch Bumper to protect your home items.
• Include cliff detection sensors to avoid drop-offs.

If you know other difference between Roomba 660 and 780, please share below.