There are limits to the depth of carpet any robot can handle, but the 4 inch compared to 3 inch wheels on the 9000 Powerbots, plus better tread (and even flexible rims on the top 9350), gives the greatest possibility and why I used it, to improve on previous Neato's. You would have to try it on the particular flooring. I have found the Powerbot the only one (compared to Neato and Roomba), which can move on "the Premium Wamsutta Fluffy Bath Rugs" (though unless the edge is fastened down, it will push that up).
The 7000 series has smaller wheels I think but still a better tread. There are no reports on carpet ability, but looks good in videos. Samsung specifies an actual height limit in the fine print of the manual (unusual disclosure for the industry), fairly conservative 1cm, I expect can be exceeded but don't have materials to refine the measure.
Long thread shag rugs have always been the worst situation for robots.
Besides depth of pile a slippery problem can occur with carpet, sometimes emerging only over time or in certain seasons maybe humidity related, and with waxy material in some carpet fibers, maybe for stain resistance. Performance of Neato's can sometimes be improved by adding a cardboard lifting slider underneath; see "Slick Carpet Effect" thread in the Neato forum. This worked for the
Botvac on medium pile slick carpet, but when all new wall-to-wall carpet was installed after a pipe break flood, I upgraded to the Powerbot 9250, also to get more thorough carpet cleaning normally needing a full size vac, for embedded dirt. The Powerbot also is able to maintain the carpet, with tests of left-overs with the regular vac; I am not sure any other robot, besides the Dyson and recent imitations by Bosch and LG, would do that. The Powerbot has a good intake design flat on the floor like a regular vac (see the VR9000 thread for intensive analysis of this design).
The weakness of the Powerbot is a software limitation in interpreting the wheel extension sensors, which sometimes causes shut downs against furniture legs when one side is raised (failing to notice the opposite side is not). This is easily corrected by disabling the sensors, without opening the case. The bumper also does not extend back as far along the side as on the 7000, series, sometimes allowing the robot to climb things it cannot get off. See thread here "Powerbot Side Bumper Extension and Tilt Reduction Mod" thread for details.
Years ago the now discontinued Electrolux Trilobite was known for its larger wheels similar to the Powerbot today.
I also find the washable filter especially attractive compared to buying supplies for other robots. The 9250 and 9350 also has a sensor and indicator for clogging the filter in case that occurs before the large bin is full, as some fine dust gets onto it.