From what i've heard, read, and watched Full Metal Alchemist follows the Manga up to a certain point. After that point they deviate from the original material because the Manga wasn't finished yet. That's why we saw sloth as Ed's mother, and Fuhrer Bradly being defeated by mustang. It's also why most of the Homunculi were defeated using their remains of when they were human.

The FMA story was a good one imho even though it deviated from the manga originally.

Key Points:

1. There were two central figures instead of just one being Dante and Van Hohenheim being the other one. In FMA they are both people that exist long ago with extreme knowledge of the alchemical processes. They use this knowledge to jump from body to body prolonging their eternal lives with Hohenheim giving up.

2. Homonculi are created through human transmutation spells with Ed and Al's mother being sloth I believe.

3. The ending is different where Ed is left on the other side which resulted in the Conqueror of Shimbala movie being made to tie up loose ends.

This is a more faithful adaptation of the Manga since it was close to being finished. Think the author of the Manga had 8 to 12 chapters left while work begun on the anime FMA: Brotherhood. Here things are much more darker than the first anime as it deals with philosophical elements, political Coups, genocide, and the lust/obsession for power. It's also here that the creation of the Homunculi are extremely different than the FMA one. (Won't spoil it)