I say the 2003 version of Fullmetal Alchemist is the better one overall. It draws you in much better than Brotherhood.
The things to keep in mind about the 2003 version diverging from the manga are twofold: First, the manga was literally still being written at the time, so they're not fucking around out of disrespect or anything like that. Second, the divergence was done with the input and blessing of the original author, so it still has that authentic feel.
It's got a couple of filler episodes with minor plotlines that don't come up again and are just there to expound a bit on ideas. Ideas like the Elric brothers' fame being used by others for their own gain, or something about getting so obsessed over something to the point where it ruins lives. They're still thematically appropriate, it's just that the characters introduced in those episodes don't end up being important in the larger plot.
Brotherhood had a very wide story. This feels like a weakness compared to the depth the 2003 version had. There were far more characters, and we kept switching between them when I was just starting to really enjoy what the current focus characters were doing. I never really cared that much about Scar's plotline in Brotherhood (though I could see some potential in it if it was done as a side story manga and the cast was explored in more depth.), and I never gave two shits about the human chimera soldiers later on. Most of the latter parts of Brotherhood, after it went a different direction from the 2003 version, felt shallow and lacking compared to the 2003 iteration.
For the moment, I'm working my way through Darker than Black, and Babylon 5. I'm also keeping up with Overlord Season 2. I read all the light novels I could find, but it's still nice to see things getting animated.
I'm at Episode 15 of Darker than Black, right after the opening visuals changed. So far, my impressions are that the dub is superb, the worldbuilding is subtle and well-done, and that the main character has a believable set of skills. He's effective at what he does, but not so overpowered that he stops fitting in with the world around him.