Here are some key difference between Roomba 770 and 650.
Roomba 770 vs 650
images from manufacturer

Cleaning System
The 650 employs the AeroVac Cleaning System whereas the 770 employs the AeroVac Series 2 Cleaning System.
According to iRobot, the 770 uses a new cleaning head that is designed with pets in mind, however, users say that there is no apparent difference on the performance.

Dirt Detect
The 650 features Dirt Detect Series 1 which use acoustic sensors to find dirt and debris whereas the 770 features Dirt Detect Series 2 With Persistent Pass Cleaning Method that uses acoustic and optical sensors to find dirt and debris, and spends more time cleaning spots where it find more dirt.
According to user reviews, the Series 2 works better than the Series 1.

Filtration
You will note the difference on the filter system when comparing them, the 650 uses 1 larger standard AeroVac Filter whereas the 770 employs 2 small HEPA Air Filters to replace the larger filter, HEPA filter can capture more fine particles and leave cleaner air behind.
The filter materials for the 770 feels better than that on the 650.

Full Bin Indicator
The 770 features a Full Bin Indicator that tells you when the bin is full and needs to be emptied whereas the 650 does not have this indicator.

Bin
The 650 uses AeroVac Series 1 Bin whereas the 770 uses AeroVac Series 2 Bin.

Extended-Life Power Management
The 770 has the Extended-Life Power Management software to deliver up to 50% longer battery life whereas the 650 does not feature.

Remote Control
The 770 comes with a Remote Control whereas the 650 does not include.
This kit is not that practical.

Accessories
The 650 comes with 1 auto virtual wall while the 770 comes with 2. The virtual wall is useful for keeping the Roomba out of off-limits areas.
The 650 comes with 1 flat brush cleaning tool while the 770 comes with 1 flat brush cleaning tool and 1 round brush cleaning tool.
The 650 comes with 1 Extra AeroVac Filter while the 770 comes with 1 Extra Set of HEPA Filters (2 filters).

Appearance
As you can see from the product pictures, they have different faceplate designs.

Price
The Roomba 650 is $100 cheaper than the 770 which is priced at $499.99 at store.irobot.com.

Dimensions and Weight
The 650 weighs 7.9 lbs, measures 13.39 inches in diameter, 3.62 inches in height.
The 770 weighs 8.4 lbs, measures 13.9 inches in diameter, 3.6 inches in height.

Both of them feature the on-board scheduling; but they do NOT support Lighthouse, so no room to room navigation.

Discuss below if you know more detail about them.

The difference between Roomba 780 and 870 are as follows.
Major Ones: Control Pannel, Cleaning System, Filtration, Bin, Lighthouse Compatibility.

Roomba 870 vs 780
images from manufacturer

Control Panel
One of the difference between these iRobot vacuum cleaners is the control panel, the 780 uses Touchpad Control whereas the 870 employs Button Control.

Cleaning System
They use different cleaning system.
The 780 uses AeroVac Series 2 Cleaning System whereas the 870 uses the AeroForce Performance Cleaning System.
According to iRobot, the new system creates more powerful suction and the brushless design reduces the maintenance to minimum.

Filtration
The 780 uses 2 Small HEPA Air Filters versus Single Large HEPA filter on the 870.

Bin
The 780 uses the AeroVac Series 2 Bin whereas the 870 uses the sealed, HEPA-filtered bin that is larger and easier to clean.

Lighthouse Compatibility
The 780 supports the Virtual Wall Lighthouse that help navigate the Roomba to clean from room to room whereas the 870 does not support the Lighthouse.

Charging
The 780 uses a Battery Charger and a Compact Self-Charging Home Base whereas the 870 uses the Integrated Home Base.

Battery
The 780 uses the Advanced Power System Battery whereas the 870 uses the XLife Extended Life Battery that was claimed to have longer lifespan.
The Xlife battery is $10 more expensive than the APS battery, and it is compatible with the 780.

Accessories
The 780 comes with a Remote Control that the 870 does not include.
The 780 comes with 2 Virtual Wall Lighthouses whereas the 870 comes with 2 Virtual Walls.
The 780 comes with 2 brush cleaning tools (Round and Flat) to clean the bristle brush whereas the 870 does not include.
The 780 comes with 1 Extra Bristle Brush, 1 Flexible Brush and 1 Side Brush whereas the 870 does not comes with any extra extractors or side brushes.
The 780 comes with 1 extra HEPA filter set (2 filters) where the 870 comes with 1 Extra HEPA filter.

Similarities:
priced at $599.99 at irobot.com,
features Full Bin Indicator to tell you when to empty the bin,
have scheduling function,
auto docking and recharging,
Dirt Detect Series 2 that uses acoustic and optical sensors to find dirt,
Persistent Pass Cleaning Method to clean dirtier spots with more time,
weighs 8.4 lbs,
13.9 inches in diameter, 3.6 inches in height,

If you know other difference between Roomba 870 or 780, please share below.

The difference between Roomba 770 and Roomba 870 are as follows.
Big Ones: Cleaning System, Filtration, Bin.

Roomba 870 vs 770
images from manufacturer

Cleaning System
They use different cleaning system.
The 770 uses AeroVac Series 2 Cleaning System whereas the 870 uses the AeroForce Performance Cleaning System which was claimed to be more powerful and requires less maintenance.
As part of the cleaning system, the 870 uses 2 brushless rubbery extractors to replace 1 bristle brush and 1 rubber brush on the 770.

Filtration
Both of them use HEPA filtration, however, they are different. The 770 uses Dual HEPA Air Filters that are smaller whereas the 870 uses single larger HEPA filter.

Bin
The sealed, HEPA-filtered bin on the 870 is larger than the AeroVac Series 2 Bin on the 770. According to user reviews, it is easier to clean the 870 bin.

Price
There is a $100 difference in price.
The Roomba 770 is $100 cheaper than the Roomba 870 which is price at $599.99 at irobot.com.

Home Base
The 770 uses a Battery Charger and a Compact Self-Charging Home Base whereas the 870 uses the Integrated Home Base.

Battery
The 770 uses the Advanced Power System Battery whereas the 870 uses the XLife Extended Life Battery that was claimed to have longer lifespan.

Accessories
The 770 comes with a Remote Control that allows you to control Roomba without getting up whereas the 870 does not include.
Both of them comes with 2 virtual walls, however, the 870 includes C batteries for the virtual walls whereas the 770 does not include.
The 770 includes 2 brush cleaning tools for removing hair and debris from the bristle brush that the 870 does not include.

Similarities:
Features Full Bin Indicator
on-board scheduling,
self docking and charging,
Dirt Detect Series 2 with Persistent Pass Cleaning Method,
weighs 8.4 lbs, 13.9 inches in diameter, 3.6 inches in height,
no room to room navigation.

If you know more difference between Roomba 770 or 870, please share below, thank you.

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.

image from manufacturer

The iRobot Roomba 871 is sold at Japan only at this moment, you can find it here http://store.irobot-jp.com/item/871.html. It is very similar to the Roomba 870, same AeroForce Performance Cleaning System, HEPA filter and Bin, Xlife Battery, Integrated Home Base, NO Lighthouse, etc. The only difference between Roomba 870 and 871 is the accessories they come with.
The 870 comes with 2 virtual walls and 1 extra HEPA filter whereas the 871 comes with 1 virtual wall and no extra filter.
Otherwise, they are the same.