The major difference between Roomba 650 and 595 are the carrying handle and included accessories.
Roomba 595 vs 650
images from manufacturer

Carrying Handle
On the faceplate, you can find that the 650 adds a recessed carrying handle while the 595 does not have.

Accessories
The 595 comes with more accessories.
The 595 comes with 2 Virtual Walls with 4 Duracell C batteries while the 650 comes with 1 Virtual Wall without C batteries.
The 595 comes with 4 AeroVac filters whereas the 650 comes with 1 AeroVac filter.
The 595 comes with 3 Side Brushes, 3 Rubber Brushes, 3 Bristle Brushes while the 650 comes with 1 Side Brush, 1 Rubber Brush, 1 Bristle Brush.
The 595 comes with 1 Round and 1 Flat brush cleaning tools while the 650 comes with 1 Flat brush cleaning tool.

Price
The 595 has been discontinued, it was sold at $299.99 at Costco and the official site did not sell this model while the 650 costs $399.99 at irobot.com.

If you know more difference between the Roomba 595 and 650, please share below.