The thing that made MM so popular back then was the number of members they had with such diverse personalities. Someone for every fan, their songs were also pretty fun and had everyone going crazy for.
Over time even though their popularity decreased, the thing that most fans liked about them was their talent in singing and dancing live, something which some fans thought AKB were not capable of doing because their management or production teams making them lip-synch in most shows.
AKB has a lot going for them in terms of fan service and interacting a lot with fans which is how or one part of them in becoming popular as well as being backed up by a pretty important and famous company, pretty much why they were on every music and variety show. Now that they have made a name for themselves they are easily recognisable which was just how MM was back 10 or so years ago, everyone knowing who they were and even to the extent of what type of character they had.
At the moment the girls are going up the ranks in popularity as people do tend to recognise them for their dance and singing abilities as their predecessors, however they still need to keep a strong grasp on letting people know who exactly each member is.
For me I was attracted to the group because of their characters and overtime I really enjoyed how powerful their lives were which I feel has carried on even to the new gen, though there are still some weak singers even someone like Ikuta and Akane have really improved in these few years they have been in the group.
This of course is just my opinion.