The art style is chibi initially (which could be off-putting to some). There is no actual cohesive story to it (but it does have some continuity to it), as it's a just-for-fun parody using the personalities and stuff of the characters, and it does assume you've watched Haruhi already. I think it does still have the hare hare yukai, but I think it might only have a spoof of it. Best part is each episode is only about 5 minutes long, and there's only 25 episodes, so it's a very quick watch.
Oh, and Haruhi's theories and ideas are considerably more wacky in Haruni-chan.