Mai Otome is the not-quite-but-maybe sequel to Mai Hime. I say that, because it seems much like an AU, but with vague hints that it's connected somehow to the former series (watch and decide for yourself).
It takes place far into the future, on the world of Earl, which has been colonized previously by Earth. 300 years after, the peace of the world is ensured by Otome; super-powered females who serve as bodyguard servants to royalty and high-ranking officials. Each Otome is bound to a person, and when either loses their life, the other will, too. It's a fairly brilliant way to ensure the peace, as any leader who goes to war literally risks their own life, since 1 Otome can easily decimate a normal army. Garderobe is the school that trains Otome, being neutral in the affairs of other countries, who meet at the school he other countries all meet there to decide things related to the school (such as how many otome each country could possess).
Now enter Arika Yumimeya, who wants to enroll in the school because she believes her mother was an Otome and wants to find her. Arika's story, and the grander political backdrop, will intertwine in a fairly well-done plot that doesn't pull any punches. In addition to death (some characters you might get attached to will die), there is another aspect explored; you see, the nanomachines that make up an Otome's power, are vulnerable to a Prostate-Specific Antigen, and if an Otome gets it in her system via sex with a male, the nanomachines dissolve and her body builds an immunity to them, making her unable to receive the nanomachines ever again.
This aspect is explored several ways, as various girls(and guys) much choose between love and duty, with some opting for female/female relationships. And the prospect of rape to remove an Otome's powers is addressed as well; like I said before, it doesn't pull any punches. That said, there may be a few things that might squick you out, depending on what kind of person you are, as one character does develop a "daddy complex." They aren't blood related, however.
The weakest category due to not quite enough battle sequences, but what they do have is fairly decent. There are no blatant flaws, and in particular I found much amused in the animation of Arika's pigtails who almost seem like characters in their own right (at least in the more comedic instances).The rest is fairly standard fare, but it does its job well. The Otome transformation sequences where they put on their robe (armor) is fairly short, so even if some is reused, it doesn't feel overdone. While we're on the topic of robes, I do like that the vast majority of their robe armor is practical and functional. It looks nice, and doesn't really play to fanservice much but seems more practical in nature; even things like ribbons and bows serve multiple combat functions.
There are various themes that really enhance the moods, particularly the haunting female chanting that happens during the more emotional moments; you really have to see for yourself. The operatic chant, almost latin in nature, that happens when most Otome transform or go into battle, is quite a refreshing break from normal magical girl fare, really driving home the point that these are majestic adults going into battle, and they're about to kick some ass.
This is what really sold it for me. While the anime starts out light-hearted and almost comedic, the drama that begins to ramp up and challenge the characters, really defines them. From Arika's naivte regarding Otome, to Nina struggling to reconcile her dreams of being an Otome, versus her feelings for her adoptive father. The most memorable one, though, I thought, was Mashiro. Starting her journey as a spoiled princess(yes, you might want to bitch slap her a few times), she faces harsh trials later on that really mature her as a character, bringing her into her own and making her understand what it means to be a queen. The layered manipulations and betrayal against the political backdrop of differing ideals on what it takes to maintain peace will give you pause, making you wonder just who is right.
Mai Otome brings back several similar themes from Mai Hime. Primarily, the multiple factions tugging from various angles, the idea of love/important persons, with the "magical" girls trapped in the middle (I say that in quotes, since their powers seem to be more technological in nature in this one). The humor is improved, and the series never feels the initial slow-pace that seemed to turn many off Mai Hime. Mai Otome adds a larger political feel, however. While the series can be watched as a stand-alone apart from Mai Hime, those who have watched the earlier show will catch a lot of references that will aid understanding.
So regardless of whether you have watched Mai Hime or not, Mai Otome is worth a look. I do reccomend watching Mai Hime first so you can catch the references, and it is a good series in its own right, but Mai Otome can stand as its own adventure. Humor, drama, tragedy, betrayal, interspersed with many heartwarming moments await those who venture within. It's also one of those series that you'll want to watch more than once to truly catch everything, as a lot of earlier things make more sense once you understand the later context.