I disliked ( a little ) the concept of another world behind the door. I don't know, it sounded too lame for me ^_^.
But the worst thing of the anime i really hated the most is the ending of the FMA OVA. My God, they kept Winry waiting..... How cruel are them :(.
Besides that, the anime is great. But manga is better IMHO
I like both the manga and the anime, but there are some elements that that make me like one more than the other.
Things that I liked in the anime
Ed's character development
Scar didn't kill Winry's parents and his friendship with Al
Lust's character in general (I felt sorry for her)
Envy's relationship with Ed and his backstory
Roy Mustang and his group
Hohenheim's return and Ed & Al's reaction to his return
Things I liked in the manga
Roy Mustang and his group
No Dante, but "Father"
The evil plot for the country
Mei-chan and her pet panda Xioa Mei
More info on Ishbal
King Bradley being Wrath and not that little annoying kid
Sloth is so cute!
Pride's identity!! OMFG!!
There are some aspect in anime I liked, like not using that much visual gags as in manga (they don't translate well to other media). But still, I hate 2003 version, and here I list some reason why:
1) Keeping beginning same as in manga. If you want to tell different story, tell DIFFERENT story.
2) Scar. In manga he was total badass but in anime he was more wimp than spirit of vengeance.
3) That door and different dimensions. Just WHY. Alchemy get energy from life of people in other dimension, where they don't have alchemy. The point of alchemy is that it's science, not magic, so it doesn't make sense not being able to use it in other dimension.
4) Homunculus origin. Again, alchemy is science, not magic. You need better reason to get homunculus to story.
5) Red stone. What was that thing? Why not go with Philosopher's Stone like in manga? And why homunculus had load of red stone in they, where's the enegy came from?
6) Homunculus weakness. Once again, ALCHEMY IS SCIENCE, NOT MAGIC!
7) Winry's reaction when she learned who killed her parents. In manga they showed how she have suffered from losing her parents and her understandable hatred toward person who is responsable from that. In anime she was like "Oh, he's a good person. Let's leave it in that".
8) Rape of Rose. Why add that? You could tell the story without rape. And if you add rape to your story, you better handle it well. In anime it was only like rape->that's bad thing->let's never talk about it again. To me it seemed like they used rape as a useless plot point as something that happens to women. And I hate it.
9) Homunculus wanting to be humans. Why would they want to be humans, after all they already are humans (artificially made, but still). In manga Hohenheim wanted to be mortal human, but there it was explained why that is. In anime it was just angst, what lead me to...
10) Angst. Some says there was great character development, but to me it seemed like constant angst.
11) Philosopher's Stone. My god that was useless shit. Over 7000 soldiers were sacrificed to make that thing, but in the end it was more or less useless, and nothing was gained for that.
12) Army was just some big scary thingy.
13) Kimblee. He was just so boring character.
14) Dante's motive. She wanted immortality, how original.
15) Sloth and Wrath. WTF! They made no sense. Why's her name even is Sloth? Why she could turn to water (her power make no sense in light of others homunculus power)? Why can't homunculus use alchemy other than Wrath (IT'S FUCKING SCIENCE, NOT MAGIC)?
16) Ending. What a anticlimactic load of BS. Al saved Ed but disappeared (WHAT ABOUT THE STONE), then Ed brought Al back but went to other dimension. Bradley died in boring and stupid fight with Mustang (why to fight in cellar, when Bradley have advance in close combat). Then parliament take power, because military nations turns to democracy that easily (facepalm). Dante died off screen with no impact to anyone. Al losed part of his memory (WHY! How can you trade memories for anything?).
There's more reason, but those are reason that came to mind right now. Of course if none of those thing bothered you and you like 2003 version, good for you. This is just my personal opinion, and you can freely disagreed with me.
I really hate the anime, especiaaly in the movie anime, alphonse is so coward, its suck man
he should be calm and cool, the plot is very differet to, in the anime gluttony became very powerfull, he eat everything and ended more powerfull
thats ridiculous, cost everythinghe ate should sent into another dimension, not store in his body.
and since the first movie I don't wanna watch the anime version anymore