[MrForbes]

Another issue with both omni and mecanum drive, is that the robot would work better with some type of suspension, especially since there are "lumps" in the arena floor surface near the walls and overpass supports.

Without suspension, the robot will drive erratically when the weight on any wheel drops significantly, such as when driving over any bump that would lift a wheel off the floor. Both of these drivetrains work because all the wheels work "against" each other, the result is that it goes the way you want it to. If you lose traction on a wheel, that wheel won't be pushing the robot the direction it is supposed to, so the robot will go wonky...