i only have experience with the MOE, MOE+, MOE K and MOE SL.
the MOE and MOE+ have a more typical AR grip angle and are fat, with my medium hands i felt they were to fat, the rubber coating of the + version is much better than the standard MOE texture.
the MOE K and MOE SL both have the same angle that is more vertical for use with short length of pull stocks, they are also thinner and use magpul's TSP texture which is much better than the standard MOE.
the K has no beavertail and also has it's centerline pushed forward putting your hand much closer to the controls, goes well with my LWRC UCIW stock for a short but comfortable lower setup.
judging from magpul's description on the MIAD it's a good choice if the MOE or MOE+ isn't big enough. and the MOE K2 is good if you want the more vertical grip angle of the SL or K but with a fatter grip.