The Sins, homunculi themed around the seven deadly sins, are among Fullmetal Alchemist's most popular characters, but between the original 2003 anime and Fullmetal Alchemist Brotherhood, some of those Sins are pretty different. Which Sins are totally different characters across the franchise, and why do these in particular differ?
Homunculi are created beings rather than naturally born, and in Brotherhood (and the Fullmetal Alchemist manga), they take after the seven deadly sins because they're meant to represent those aspects of the villain. In the first anime, however, Homunculi work rather differently; instead of being aspects of the villain, each Sin represents an attempt at reviving a dead person via human transmutation. The differences arose because the first anime caught up to the manga, and was forced to either go on hiatus indefinitely, or create an ending of its own. At the time, they knew there were supposed to be seven Sins, of course, but only had information about five of them, so they had to create the remaining two from scratch.
The Sins that differ most are those two: Sloth and Wrath. In Brotherhood, Sloth is a giant with exceptionally powerful muscles who spends a lot of time digging. In the 2003 anime, however, Sloth is based on Ed and Al's mother, and was created as a result of their own failed attempt at human transmutation. She uses water-based powers and is surprisingly strong. Wrath is a child in possession of Ed's real arm and leg, based upon the baby which Izumi Curtis tried to revive. He considers Sloth to be his mother, so the two are strongly connected. Wrath in Brotherhood is actually the secret identity of King Bradley, the leader of Amestris. The writers of the 2003 Fullmetal Alchemist knew Bradley was a Homunculus, but didn't know which, so in that series Bradley is instead secretly Pride.
The Homunculi Differ in Brotherhood in Other Ways, Too
In a coincidence, both sets of Sins have a child among their number: Wrath in the 2003 anime, and Pride in Brotherhood, who takes the form of Bradley's son Saleem. Saleem isn't a Homunculus at all in the 2003 anime, though he does appear. There's also Greed, who is the only Homunculi to be replaced in the story of Brotherhood. The original Greed does appear in the 2003 anime, although his abilities and personality are slightly different, but the second Greed possesses the body of a Brotherhood-exclusive character named Ling, and is thus absent. Envy's lizard-like true form is also absent from the 2003 anime, although Envy does take on a draconic appearance that's vaguely similar in the film Conqueror of Shambala. Instead, Envy's true form is said to be that of the person he was based on: Hohenheim's son from hundreds of years earlier, thus making him Edward and Alphonse Elric's half-brother in that continuity.
The Homunculi from the 2003 Fullmetal Alchemist anime were complex characters who had no trouble garnering a fanbase, so it's little surprise that both versions retain some popularity. While some today might say to only watch Brotherhood, the different Homunculi are one of the most compelling reasons to check out the first anime.