Fullmetal Alchemist is an odd beast for an anime. There have been plenty of anime series that were adapted from still ongoing manga, caught up to that source material, and created their own ending. However, the anomaly is a series still being so popular by the time the manga did end five years later to merit another adaptation.
That’s what happened with the original Fullmetal Alchemist anime and Fullmetal Alchemist: Brotherhood.
While it is well known that the original Fullmetal Alchemist anime is a poor adaptation of its manga source material, Fullmetal Alchemist: Brotherhood, while vastly superior and adapting the manga ending, also has a few flaws itself, truth be told. Enough to merit writing this to explain them, anyway.
If you watched the original Fullmetal Alchemist anime, the anime diverges from the manga in full at Episode 34, which is Chapter 29 in the manga. However, even before that, there were tons of changes to the Fullmetal Alchemist story in order to sort of buy some time.
As for Fullmetal Alchemist: Brotherhood, it adapts the full story and the actual ending to the manga series. However, it does skip a few small events and most of the omakes because they are fluff and comedy.
You will note that, perhaps because they presented much of that in the original FMA, the first seven volumes of the manga are fairly shortened in Brotherhood and events are re-ordered – perhaps to make them more interesting to the people who had already seen the original series.
If you are looking to see the events skipped, you can find a list of them here in full from the wiki. As for chapters to consider reading to cover the events not seen in either the original FMA or Brotherhood, I would recommend Chapters: 3, 4, (the cut/abbreviated Youswell Incident) 27 (Omitted adventure where Ed goes to South City to turn in his assessment report) 37, 38, 39, (a cut fight between Ling and Lan Fan V. Envy and Gluttony).
Really I recommend reading the manga for all the omakes and extra bits. They are comedy, but they are interesting, if not just cute. You do see a few of them in the original FMA anime, however.
