Another difference which has not been noted here between Mecanum and what OP refers to as PMM: With the same motors, gearing, and wheel size, Mecanum accelerates 41% better than PMM, while PMM has a 41% higher free speed than Mecanum.
The big advantage of Mecanum over PMM, imho is that (now that both omni and mecanum wheels are available as COTS items), construction of the mecanum chassis is much easier; there is no need for any 45° chassis members. The KoP drivetrain actually has mount points for four TB-micro to support mecanum. You could also build a chassis using versaframe or WCP COTS components without any 45° gussets to be mecanum.
A wrinkle on PMM I experimented with a couple of years ago is one I called Pakuni Drive†, named after the simian aliens from Land of the Lost and their attribute of walking forwards like humans, but running sideways like my little brother Vernon when he was 18 months old. The idea is that I toed in the wheels ~22.5° rather than 45°. (It turns out that the acute angle on a 5-12-13 right triangle is closer to 22.62°, so that’s what I really did.) Anyway, this gives a forward acceleration which is 2.4x better in the forward direction than the lateral (strafe) direction, but a free speed which is 2.4x better in the lateral. My intention was to start the robot accelerating in the “forward” direction, then rotate the robot 90 degrees to “shift” to a speed 2.4x as fast for longer (cross-field) runs. My attempts with an arduino and no gyro or other feedback nor radio input were unsuccessful, so I’m putting the concept out there in case anyone wants to try this with better control systems.
† My earlier name for this before inspiration hit was roto-shifter, as will be explained in later sentences.