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.