So in summary: Just watch Brotherhood.
Or read the manga
And I don't want to bash FMA 03, it's a perfectly good anime despite it's quirks and flaws. Some quick positive/negatives comparing the manga/brotherhood story to the 03 version
What I liked that 03 did differently
+Conceptually the idea of the homonculi being born from failed human transmutation was great, but they should have flat out dropped the deadly sins naming convention as it doesn't work when only half the homonculi match said sins. They also left poor Gluttony and (kinda) Pride without an alchemist to be connected to.
+Even if the filler wasn't always great the slower paced opening because of said filler allowed us to establish Ed, Al, and the rest of the cast really well before shit hits the fan when Hughes dies. Even in the manga his death happens really early in the story and I can appreciate them extending his life the way they did.
+The idea that equivalent exchange may not be real is a interesting idea that (again) the series never explores enough with.
+Lust expanded role in the story worked really well and she's by far the best handled homonculi in terms of being based upon a real human and the conflict within her of what she is.
-Roy's character on the flip side was completely botched, his characterization was all over the place and he never got to have any great bad ass moments like he does in the manga/brotherhood. His one signature moment fighting Bradley is pretty disappointing for the big final fight of the series.
-Anytime original filler was written by Bones it was god awful, particularly the fake brothers was a plot line that was awful and went no where outside of being a dues ex machina for Ed to find Dante's hideout.
-Dante is an awful villain and an awful character who simply exist in the plot to give the story a evil mastermind. The problem is Dante never comes off as charismatic or powerful enough to do the things she's credited with doing. The character either needed a complete rewrite or more scenes depicting her as a master manipulator.
-The other world concept also needed to either be scrapped completely or completely rewritten and introduced WAAAAAAY earlier in the plot. Especially when it seems to contradict the laws of the story up to that point. Ed and Izumi passed thought he gate along with other alchemist attempting human transmutation, they saw the truth, paid a price, and gained the power to transmute without a circle, all of the sudden passing though the gate takes you to another world? What?
If the gate was meant to be a portal between the two worlds then human transmutation should pull the person from the other world into the Alchemist world. This would have created an interesting mechanic of the homonculi actually being the same versions of people from our world and perhaps their motivation would have been trying to find a way back home but having no way to access the gate because they can't use alchemy.
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FMA 03 has a lot of great ideas and a lot of great moments, but clearly the story needed a bit more refinement before it was finished. I'd say it's a solid 4/5 mostly hurt by the last 5ish episodes where things fall apart quickly and often.