I'm gonna get shit for writing this, but in my opinion Utena is not nearly as good as people make it out to be.
Utena seems to be another case parallel to that of Evangelion, where it has received massive praise as being extremely deep, yet this seems to be people just masturbating their ego and pretending they understand something better than others, despite never presenting an argument for it being deep that isn't either massively pretentious or pretending some simple concept is doctorate level philosophy.
Enough of that though, let's start off with what the show did right.

The Good
The music is incredible. It's absolutely the most standout thing about the show. There are tracks that are showy and grab your attention, such as Absolute Destiny Apocalypse and the show's opening, but most of the tracks are simply unique and well crafted background music which blends perfectly with every part of the show. One thing I must commend the soundtrack on is how each fight has unique lyrics, although they seem random at times and aren't all that relevant to the character fighting Utena.
The second good aspect of the show is the art, particularly of the backgrounds and setting. While the character designs aren't bad, what really stand out about the art is the way it makes the environments feel real, and at times, surreal. There's tons of detail put into all of the environmental designs in the show, which makes it less upsetting when the same art and animations are used several times. Not just backgrounds but also interesting imagery, similar to what you might see in a Shaft anime. For example, the scenes before each fight where A-ko, B-ko, and C-ko play out some skit always have a unique artistic presentation if nothing else.
That said, if I simply wanted to see good imagery and hear good music, I would watch a music video. At the end of a day, these are supposed to be toppings on the cake, and it doesn't matter if they're great if the cake itself isn't as well.

The Bad To start, the entire concept of the show is without reason. We're never given a reason as to why winning a certain amount of duels should give someone the power of revolution, nor why this person has to be engaged to the rose bride. The audience is just supposed to go along with it because the characters said so. Not to mention the fact that the power of revolution is extremely vague and never expanded upon. Utena has a nasty habit of being incredibly repetitive, and as such, becomes predictable. For example, in the first arc we can predict that Utena will meet and duel each of the student council members. In the second arc, the Black Rose Society finds people close to the student council and makes them duelists who then fight Utena. In the third arc, the student council members get frustrated with the End of the World but then are convinced to fight again once Touga introduces them to Akio. At least in the first arc, the way Utena meets each student council member is varied and the way the episodes play out isn't predictable. In the latter two arcs, though, the way things unfold happen extremely similarly to each other. Not only are certain lines repeated verbatim, but the fights in these arcs almost all play out in the same way. The fights are further weakened by the fact that before each fight there's two and a half minutes of reused animation every time (reaching the arena and acquiring the sword). Some of the episodes are really weak. For example, Keiko's episode was predictable and played on an uninteresting relationship which would never get fleshed out any further. The way some of the dialogue and characters are is written like a fucking fanfiction. Minor characters have so little depth and don't even seem like real people. Most of the generic students of the school are there solely to gossip and say rude things about people. The named characters of lesser importance are generally irrelevant until they have their one episode about them, and after that episode is done they fade back into irrelevance again. Even some of the main characters are mostly one-dimensional. Saiyonji, Miki, Nanami, and even Utena herself are characters who are generally very predictable and transparent. A character doesn't need to be incredibly deep in order to be a good character, but if all of a show's characters are one-dimensional then it starts to become a problem, especially in the case of a show which is praised for its depth. The show is horribly vain, which isn't something I would usually make a point to complain about, but it's so present in Utena that it's impossible to ignore. The perfect example of this is Nanami, who is ridiculously vain and rude to everyone. People like Nanami simply because she's rich, pretty, and Touya's sister. She finds it fit to hold a party simply to show off a new expensive piece of jewelry she got. This would have worked too, if it weren't for Juri showing up with an even more expensive piece of jewelry which everyone at the party then fawns over.Conclusion Utena is a show in which a large amount of the content doesn't add nearly enough to its overall quality. While the story becomes fairly interesting at around episode 33, you have to sit through over thirty episodes of repetitive content in order to make it that far. While the characters aren't terrible, most of them are fairly simple and, at times, generic. The music and art do a good job of creating a unique and interesting atmosphere for the show, but an overabundance of forgettable fights and uninteresting episodes make Utena feel like somewhat of a waste of time.