The biggest difference between the two is how they navigate and clean. The Roomba uses a series of sensors located on the bumper and underneath that help the robot detect the presence of walls, obstacles and drop off points (e.g. stairs). The Roomba doesn’t try to avoid obstacles instead it bumps into them and goes in a random direction. It does have a wall sensor that detects walls that helps it follow its path and clean edges.
Neato has a more polished navigation system that maps a room out and starts of by cleaning the perimeter then slowly cleans the interior areas in straight overlapping passes and while the Roomba bumps into objects, the Neato does its best to avoid them using a laser mounted on top.
With regards to how they clean, the Roomba uses two counter rotating brushes augmented by suction to pick up dirt and debris. In essence it is a robotic sweeper but iRobot claims that the new 880 model has a better vacuum motor with 5 times more airflow compared to previous models. Neato relies more on suction and uses a motorized brush to augment the suction which is much similar to how most traditional vacuums work.
Original Source of the Infographic: http://www.