The iRobot Roomba 980 is the latest Roomba robotic vacuum cleaner whereas the 650 is old but a good selling model.
If you are deciding between these 2 robots, the info below might help you buy the right one that fits your needs.
Here are some key differences between iRobot Roomba 980 and Roomba 650.

Price – The Roomba 980 is much more expensive than the 650.
This is one of the major things you should consider while comparing these 2 Roomba models.
The 980 is near $900 whereas the Roomba 650 is a bit over $300 on some online shopping malls at this moment (2017-03-25).
As you can see, the fact is that the 980 is too expensive for many people, with a price tag of almost $900.
If you are in a tight budget, the 650 is a better choice.

Cleaning Pattern
This is a big difference between them.
The iRobot Roomba 650 uses a random cleaning pattern whereas the 980 cleans in a systematic way.
When cleaning in a random pattern, the Roomba might miss some spots, and meantime spend too much time vacuum some other spots. With the systematic method, the 980 can vacuum more efficiently.

Mapping, Navigation and Resume Cleaning
The 980 can resume cleaning and clean an entire level of your home.
The 650 features iAdapt Navigation that utilize sensors to navigate and adapt to your changing home.
Whereas the 980 features iAdapt 2.0 Navigation and Visual Localization, with new sensors and a camera, the 980 can continually build and update its map of the cleaning enireonment, and clean an entire level of your home.
When short of battery, the 980 automatically docks and recharges, and it knows where it cleaned and where it has not cleaned, after recharging, it resume cleaning. Whereas the 650 only automatically docks and recharges. It does not continue cleaning the places it did not vacuum.
The 980 supports Multi-Room Navigation while the 650 does not.
If you have large house, then the 980 fits your needs. If you just need one to clean small room, then the 650 is enough.

Main Brush System
Both of the 980 and 650 have 2 counter rotating beaters, however, the beaters are different. The 650 uses 1 bristle brush and 1 rubber brush while the 980 uses 2 brushless extractors. The brusless extractors does reduce hair tangles and brush maintenance.

Suction Power and Carpet Boost
The 980 uses a more powerful motor which provides greater suction power. It has a Carpet Boost function which automatically increase the suction power while vacuuming carpet and rugs, the 650 does not have this Carpet Boost.

HOME App
The 980 supports the iRobot Home App.
Wi-Fi enabled, the iRobot Home App lets you control the Roomba 980 via your smart phone anytime, from anywhere. Whereas the 650 does not compatible with the Home App.

Battery
The 650 uses 3000mah NiMH battery whereas the 980 uses 3300mah lithium ion battery.

Home Base
The 650 comes with a 110V Home Base while the 980 comes with the 100-240V/50HZ-60HZ Integrated Home Base.

Filtration
The 650 uses AeroVac Filters whereas the 980 uses AeroForce High-Efficiency Filter which claimed to be able to capture 99% of allergens, pollen, and particles as small as 10 microns.

Size
The 650 is smaller and lighter.
The 650 weighs 7.9 lbs versus 8.7 lbs on the 980.
The 650 has a diameter of 13.39 inches whereas the 980 diameter is 13.8 inches.

Full Bin Indicator
The 980 has a Full Bin Indicator that the 650 does not feature.

Overall, if you have small spaces or are in a budget, then you’d better buy Roomba 650. Otherwise, go with the 980.

The iRobot Roomba 960 is a model between the 980 and 880. It is similar to the 980, such as supporting WiFi connection and having visual navigation and resume cleaning, but equipped with the Gen 2 motor that are used on the 880.
Below we will compare Roomba 960 and 880, and list some differences and similarities between them.

images from manufacturer

Difference:

Cleaning Pattern
This is a big change and the biggest difference.
The iRobot Roomba 880 uses a random cleaning pattern like other older roomba models whereas the 960 cleans in a systematic way like the 980. The 880 might go over the same area again and again, and miss some other place. The 960 is “smarter”.

Mapping and Navigation
With a camera and new sensors, the 960 can continually create and update its map of the cleaning enironment and keep tracking its location.
Whereas the 880 do not feature these.

Resume Cleaning
The 960 can resume cleaning where it has not cleaned after self charging whereas the 880 does not feature the resume cleaning, it just automatically docks and recharges.

Entire Level Cleaning
With the new mapping, visual localization, and resume features, the 960 can clean an entire level automatically. Whereas the 880 needs the help of Virtual Wall Lighthouse Devices to clean multiple rooms (up to 3 rooms) with a 25 minute limit each room, it can not resume cleaning.

Home App
The Roomba 960 is WiFi connected robotic vacuum. iRobot offers a Home App, compatible with Android and iOS, lets you control the 960 via your smart phone.
Whereas the 880 does not support WiFi connection. BTW, it comes with a remote control.

Control Button
There is also design difference on the control buttons.
The Roomba 880 has 5 buttons on the control panel, they are in 2 lines. Whereas the 960 has only 3 control buttons – Clean, Home, and Spot. And they are in a line. Functions like the schedule cleaning are controlled via the Home App now.

Battery
The 960 comes with a 2130mah lithium ion battery. According to iRobot, it runs up to 75 minutes per charge.
Whereas the 880 comes with a 3000mah XLife advanced Ni-MH battery. The running time is near to the 960.

Similarities:
They are in round shape.
Feature Aero Force 3 stage cleaning system.
They use the same Gen 2 motor that provides 5x the air power compared to Roomba 600 and 700 series AeroVac systems.
Have 2 main dual counter rotating brushless extractors incorporate a rubber tread, 1 spinning side brush, dirt detection and spot cleaning function.
Integrated Home Base (100-240V/50HZ-60HZ).

To learn more about the Roomba 960, you can download the manual from iRobot official website.
Here is the link – https://homesupport.irobot.com/euf/assets/images/faqs/roomba/960/manual/en-US.pdf
800 manual – https://homesupport.irobot.com/euf/assets/images/faqs/roomba/800/manual/en-US.pdf
If you know other difference between Roomba 960 and Roomba 880, please share below by commenting below.

Comparing these 2 iRobot Roomba vacuum cleaners, we can find that the Roomba 960 looks very similar to the Roomba 980.
In fact, they have many similarities, such as using iAdapt 2.0 Navigation with Visual Localization, being able to self recharge and resume cleaning, clean multiple rooms, clean on a schedule, support iRobot HOME App, having cliff-detection sensors, etc.

However, they are not identical. The iRobot Roomba 960 is just like the lite version of 980.
Below are some differences between Roomba 980 and 960.

images from manufacturer

Carpet Boost
The 980 has one new feature that the 960 does not have. It is the Carpet Boost.
According to iRobot, this enables the 980 to automatically increase power on carpets/rugs where dust and dirt hide.

Motor and Air Power
The 960 uses the same motor, Gen 2 motor, as the 860 and 880.
With the Gen 2 motor, the 960 generates up to 5x the air power compared to Roomba 600 and 700 series AeroVac systems.
Whereas the 980 features the new Gen 3 motor that is more powerful, it provides up to 10x the air power.

Battery and Run Time
The 960 comes with a 2130mah lithium-ion battery whereas the 980 uses 3300mah lithium-ion battery.
The 980 runs up to 120 minutes whereas the 960 runs up to 75 minutes.

Accessories
The 960 comes with only 1 Dual Mode Virtual Wall Barrier whereas the 980 comes with 2 Dual Mode Virtual Wall Barriers.

Price
The Roomba 980 is $200 more expensive than the Roomba 960.
On irobot.com, the 980 is priced at $899.99 versus $699.99 for the 960. (prices checked on 2017-03-09)

Color
The 960 is in black with silver whereas the main color of 980 is black with brown.

Weight
The 980 weighs 8.7 lbs versus 8.5 lbs on the 960.

If you know other difference between iRobot 960 and 980, please share below.