Alternative/Shoegaze
I believe that FLCL Alternative works as a sequel (or rather a prequel) to the original as it doesn't try to be the original and honestly does a pretty good job at capturing the essence of the original while having it's own redeeming merits, and with FLCL Shoegaze being an epilogue to Alternative I believe that these two seasons are more FLCL than say Grunge or Progressive. There was this conversation I had with a few people regarding a series (can't remember what it was) and I made the argument that I could appreciate its sequels because while they do have some elements of the original, they're different enough to be appreciated as it's own standalone thing and I believe this can be applied to both Alternative and Shoegaze.
Progressive/Grunge
When it comes to FLCL Progressive and Grunge, I can't exactly say the same thing that I said for Alternative and Shoegaze because both Progressive and Grunge are essentially a sequel and prequel to the original, meaning that they both are directly tied to it. While I didn't dislike Progressive and did find some enjoyment out of it, I can say that it does try to act like a successor to the original by incorporating borrowed ideas and imagery from the original but ultimately feels very loosely related to it, and I believe the fact that it takes place in Mabase years after the original only cements the fact that it's trying to be something it's not. Of note I should say that while I did like the cameos characters like Naota and Mamimi made in the ending cinematic, I for one am glad that they didn't make a full on appearance and I'd much rather that they don't make a return as I feel like their stories ended pretty decently and that there really isn't anything else that can be done with them. I really liked how ambiguous the ending of the original was and how it allowed the viewers to come up with their own thoughts on what happened to them after FLCL, and I feel like bringing them back and explain what they've been doing would kind of ruin that ambiguity, which goes to show that Progressive tried to capture the spirit of the original by including all these different elements from that but couldn't make them work as well as I would've hoped.
FLCL Grunge, for all the bad press it got I can say that I can definitely recognize on how different it was (mainly due to its visuals) though I can't say much beyond that as most of the runtime for each episode consisted of flashbacks, which isn't inherently a bad thing as it's a unique way of telling a story by having different characters recount how the exact same day went for them... if not for the fact that the season only had 3 episodes in total. I feel like it really hit its stride in its third and final episode but that's as far as it could get before the season was over. Grunge is listed as being a prequel to the original FLCL and to that I say, "Hah", because while we did see Amarao lose his eyebrows and him seeing the giant hand for the first time... it honestly doesn't feel like an actual prequel to the original because it didn't really explain much. I did enjoy it however, and feel like it really could've benefitted from an entire 6 episode season as I did like the main characters, especially the entire storyline in its final episode with Orinoko. I feel like FLCL Grunge is different enough to be viewed as its own thing but because it's working as a prequel to the original, it can't really escape the high bar that has been set by FLCL and the same can be said for Progressive as well (to some extent of course).