The iRobot Roomba 650 belongs to 600 series while the Roomba 870 belongs to 800 series and it is like a lite version of 880.

The difference between Roomba 870 and Roomba 650 are as follows.
Roomba 870 vs 650
images from manufacturer

Cost
The Roomba 650 is $200 cheaper than the Roomba 870.
The 650 is priced at $399.99 at irobot.com whereas the Roomba 870 is price at $599.99.

Cleaning System
They use hugely different cleaning system.
The 650 uses AeroVac Cleaning System whereas the 870 features the new AeroForce Performance Cleaning System which has more suction power and requires less maintenance.
As for the bottom cleaning beater, both of them have 2 counter rotating beaters, however, the beater types are different, the 650 uses 1 bristle brush and 1 rubber brush while the 870 uses 2 brushless extractors.

Battery
The 650 uses the yellow Advanced Power System (APS) Battery while the 870 uses the purple XLife Extended Life Battery, both of them are NiMH battery, however, iRobot claim that the Xlife battery doubles the lifespan.

Home Base Type
The 650 includes a battery Charger and a Home Base (110V) whereas the 870 uses the Integrated Home Base (100-240V/50HZ-60HZ) with no standalone power supply.

Virtual Wall Amounts
The 650 comes with 1 Auto Virtual Wall (requires 2 C batteries, not included) while the 870 includes 2 Virtual Walls (batteries included), both of them do not supports the Lighthouse technology.

Filter
The Roomba 650 uses a AeroVac filter while the 870 uses a HEPA filter.
Commonly, a HEPA filter emits better quality air back to your house.

Dust Bin
The 650 uses AeroVac Bin while the 870 uses a HEPA-filtered bin. The AeroVac Bin is smaller.

Full Indicator
The 870 has an indicator that tells you when to empty the bin whereas the 650 does not have a full bin indicator.

Dirt Detecting and Persistent Pass Cleaning
The 650 features Dirt Detect Series 1 that uses acoustic sensor to find dirt.
While the 870 features Dirt Detect Series 2 which uses not only acoustic but also optical sensors to find dirt.
When the 870 finds the dirtier areas, it will employs the Persistent Pass Cleaning technology which uses a back-and-forth cleaning pattern to spend more time cleaning the dirtier areas. Whereas the 650 does not feature the Persistent Pass Cleaning.

Dimensions
The 650 has a smaller diameter which is 13.39″ versus 13.9″ on the 870.

Weight
The 650 weighs 7.9 pounds versus 8.4 pounds on the 870.

Accessories
The 650 includes 1 Auto Virtual Wall with no C batteries included whereas the 870 includes 2 Virtual Wall with batteries included.
The 650 includes 1 Extra AeroVac Filter whereas the 870 includes 1 Extra HEPA Filter.
The 650 includes 1 flat brush cleaning tool that the 870 does not include. However, the brush cleaning tool is not useful for the 870 since it has no bristle beater brush.

Both of them features on-board scheduling, edge brush, self docking and charging, 1-Year limited warranty on robot, 6-month limited warranty on battery, etc.

If you own iRobot Roomba 650 or 870, or know other difference between them, please share more info below to help potential buyers to make a right purchasing decision.