I love both series because they each tickle different parts of my funny bone and evoke different forms of what I call "faux nostalgia".
I'll say omitting the actual violence done to "hyper girl" (sorry, still haven't gotten the names down) is subtle brilliance: she does something inane.. next scene she's face down somewhere.
Azumanga is more about watching the individual characters unfold and evolve through their years in high school. To some extent, Azumanga informs me about tolerating and appreciating character flaws in your comrades. I.M. just makes me smile for now --- I'll know more as the DVDs arrive.
My next task: avoid posting again til I've the girl's names straight