There are 2 or 3 reasons why I prefer the MAX-31 over the MAX-11.
First and foremost, as someone above already mentioned, the additional length and weight of the MAX-31 makes it a little steadier and easy to shoot.
Secondly, in the interest of putting less wear and tear on the expensive lower, I prefer to shoot an upper with its own feed ramp. The MAX-11 uses the M-11/9’s original feed ramp which is subject to wear and some deformation. This may not be a big deal to anyone but me, but the MAX-31 has a better designed, more robust feed ramp. See photo below. Note the wear on my original feed ramp, especially at the top.
Thirdly, the drums are often a convenience and its nice to have the option of 72 uninterrupted rounds. Moreover, with Practical Solutions excellent PS/31 Zmag Adapter, you can use your existing Z mags:
https://www.youtube.com/watch?v=DeJ0ExkpaFU
I will say that drums are a fairly minor issue for me although I realize that is the major reason the MAX-31 exists. Stick mags probably keep me from wasting ammo at a more rapid rate and they are not that much slower to load. When you factor in the time spent taking the drums apart, winding them and putting them together again, it takes me roughly 2:20 to load a drum with 72 rounds and 2:40 to load 72 rounds into 3 stick mags.