Whereabouts in the story did you get up to on the reader sites? For the time being, I can summarise events in the last volume, not counting the sidestories.

The final duel takes place in the castle that was originally hanging upside-down in the arena. The student council tried coming with Utena and Anthy, but three of them got trapped in glass coffins due to specific flaws, while Touga (who didn't get coffin'd because he wasn't "trying to run away") was injured protecting Utena from some falling rubble. By the time the last volume begins, Akio has revealed to Utena that he and Dios were once one and the same.

Akio's origin story is quite different in the manga; the Dios of the past was more like a god than just an archetypical prince, but after a certain point, his Akio aspect got sick of catering to humanity's demands and took over Dios's body for himself. Dios would have disappeared (with his last act being to save the child Utena from drowing in that river) if Anthy hadn't stepped in. She became cursed as the Rose Bride because she sealed Dios's power away in the castle to keep him alive, and his sword in her bosom as a last token of her love; there's no Million Swords of Hate in the manga.

Unfortunately, Dios was murdered by Akio in the end of volume four, making Anthy lose the will to live to the point where she literally starts to fade away. Akio tries turning this against Utena as well ("Where would you be without your prince?") but gets a well-deserved smack in the face for it. Cue duel.

Two noteworthy things about the duel: First, Utena's rose starts wrapping thorns around her before long, threatening to kill her, with Akio's explaination being that "the path of a prince is a thorny one". Second, there's no Anthy backstabbing; instead, it basically ends with a surprisingly bloody double KO as Utena and Akio slash each other across the chest.

Some melodrama happens, and eventually, Utena more-or-less takes on Dios's spirit, kisses Akio (seems like she never stopped having feelings for him in this version) and they both ascend to a higher plane of existence. After that happens, there's a very pretty page where the castle is falling away, coffins and all, and Anthy catches hold of Touga while they're all falling. It also turns out that Utena had thrown Dios's ring (which she'd been trying to get back from Akio throughout this volume) to her at the last minute.

In the end, Anthy is wearing a boy's uniform much like Utena's and is acting more like her, while she and Touga are the only ones who remember Utena anymore. (I guess Touga remembers not just because he's genuinely in love with her here, but because he was the only other duellist who didn't end up in a coffin.) Touga actually tears up when he thinks that he might never see Utena again, but Anthy tells him that Utena is still alive out there, with Dios's ring as proof, and that the revolution is still waiting to happen. Anthy leaves Ohtori, and the last two pages imply that she does indeed find Utena again. The end.

Oh, and the real chairman appears very briefly. He apparently got better.

tl;dr: It's a much more straightforward, more typically shoujo story than the anime, played more like a straight fantasy without nearly as much surrealism.

Ah, but you left out the best part -- where Saito and Ikuhara explain Utena.
Not to mention Utena's angel wings.