Seen at Drastic (there was no attribution, so I presume BigN himself wrote it):

20. Was anyone else tired of the comparisons between Lucky Star and Azumanga Daioh? Is the latter really a paragon of slice of life school comedy anime?

I understand the question was made in jest, but still... Why has nobody come with something like Azumanga so far? It was 5 long years now.

Hidamari Sketch is probably the nearest thing ever attempted to recreate Azumanga. It floundered mostly on the poor implementation quality of the anime (e.g. looked like ass most of the time with short flashes of brilliance), but otherwise was clearly made with the same aim. The 4koma was reshuffled to allow for anime pace, among other things.

The later is what Lucky Star did very poorly. Azumanga and Hidamari mostly had big episodes (even though officially Azumanga was subdivided into 5-minute shorts). Lucky Star, however, seems incapable of any flow outside of huge arcs (such as Komiket), creating tons of disconnected filler. So, even if Lucky Star were not primarily referential like Excel Saga, it would still fail to match Azumanga.

Confusingly, when I write that Manabi Straight matched Azumanga, I mean something entirely different: the overall level of greatness. Manabi is plot-driven and not episodic, so it's in entirely different camp. It does not match Azumanga as a slice of life, it has its own unique merits.