Long ago, I had a Roomba red robotic vacuum. That old model used a NiCad battery pack, which was doomed to eventual failure due to the memory charging issues. The newer models now use Lithium ion packs. The old Roomba was also not well protected against dust collecting on the circuit board, causing it to act as if it was having a seizure due to electrical shorts caused by the dust.
Currently, I have a Roomba 895, and two Neato Botvac D5. One for each floor. The 895 model uses the old non-mapping style cleaning ie. mostly random bouncing off walls and objects. Finding it's way back to the charging base depends on luck, because it needs to be in the same room and within sight of the base to detect the IR signal to home-in on. Since I have it in one small room, it is not a problem for me. Otherwise, the robot may deplete it's charge before it can find the base.
My Neato robots use the room mapping technology. They use a laser beam to calculate distances to walls and objects, then produce a map of the floor. Similar to a Zamboni, it uses a back and forth pattern to clean each room it has mapped. The newer Roomba models also map the floor layout, but last I heard it takes photos. The photos are sent to the iRobot servers where it is somehow converted into a map. The Dyson robotic vacuum also uses pictures. I am not comfortable with the idea of photographs of my home being sent out on the internet, even if iRobot claims they are secure. Would you like pictures of you stepping out of the shower sent to iRobot? Also, while the Neato can operate in total darkness, the Roomba and Dyson robots need light to take photos.
Room mapping makes it easy for robots to get back to their bases, since they know exactly where it is located on the floor map. It is amusing to see the robot drive a path directly back to it's base, going around any furniture or object it had previously mapped. The base can be hidden behind a chair, which would be a problem for non-mapping robots. They just need space to maneuver onto the base.
Overall, I prefer my Neato robots. With iRobot, you will likely need to pay extra for the iRobot name since they were the first to bring a robotic vacuum to market. Although, Electrolux was the first to develop one (the Trilobite), but it was a big clunky device that never made it past the prototype stage. The only problem I have encountered with my Neato, is occasionally it may need to be reconnected to my home wifi. eg. after my dogs dislodge it from the charging base, and the battery becomes depleted before I notice. It will send me an email telling me it needs to shutdown, but I may not notice in time. It can reconnect itself to the wifi after fully charged, but sometimes needs manual help.