Azumanga doesn't have a plot. There is nothing in Azumanga that even vaguely resembles a story. So it must be character driven, right? However, Azumanga lack conflict and character development. The show covers 3 years of their lives (High School) and after 3 years all the characters look and act the same. umm wait Chyio-chan did change her hair style by putting her pig tails lower…
The character's quirks and jokes are very funny. That is until you watch a few more episodes. Then the jokes get old and very repetitive. How many times did the same cat bite Sakaki? How many times does Koarin obsess over Sakaki? Yes, we know you are a freak that likes high school girls. The repeated use of the same quirks makes many of the characters seem shallow and one-dimensional. I mean is there anything else beyond the two, three word description you can give to each character (ie "airhead" "pervert" "smart/cute" "athletic" "energetic"). The jokes did not come from the characters, the characters themselves were the joke. What breaks this anime for me is that even the situations are repetitive. How many times did we have a Sport fest, culture fest, and beach episode? By the time I was at the 5th episode I was getting bored, ok I’ll admit there was the occasional funny scene.
Perhaps I’m being too critical on Azumanga, the source, a 4 panel comic can’t really give that much substance, right? However, I think about Lucky Star, also based on a 4 panel comic and realized how Lucky Star is superior to Azumanga in every possible way. In addition, the jokes come from the character in Lucky Star, not the character themselves being jokes.