I've been thinking that, despite the name just being awkward in roman letters (My brain writes it as Anjurumu now so I have to police myself when typing lol), the name change itself has been really important for them and just as at fault for the probable success as 3rd Gen.
S/mileage was given a very specific image. Higher toned "squeaky" voices, super genki and cute, short skirts and S/mileage badges. They had this tiny little box and every time they didn't do something within it people got annoyed. This is not even factoring in the original group losing half its members and being forced to audition more.
Sure Taiki Bansei is high energy, but it's got a lower tone and is less cutesy high energy and more like a dance party. And there are pants being worn :O! Sure as S/mileage there were some shorts at times, but people would complain about that and never pants. We have complete leg coverage. ANGERME just has so much more freedom to be whatever they(and management of course) want to be.
EDIT: Also I forgot to mention that Ayaka seems truly well invested in everyone being treated like 1st Gen. She really seems to fit seemlessly in with 3rd Gen at least and some of 2nd Gen as well. I am a bit worried about Kanon though since watching that H!S with her and 2/3 of 3rd Gen. I really did get this aura of "I am your senpai, treat me like a senpai. Give me proper respect" Since they both were former KSS though, it might just be leftover from how they used to interact and maybe that's getting better.