From what I've seen the anime and manga follow almost identical story for Magi. In the end of season 1 they made a few changes in Ali Baba's personality. Some people argue it was a screw up. However, this reddit user sums it up perfectly (Spoilers)
At the end of the first season of the anime, Alibaba falls into depravity. This event doesn't actually happen in the manga. Aside from that there are no significant differences between the two mediums. People argue that one is better than the other, however they both tell a nearly identical story. Somehow some people think that it messed up Alibaba's character, however it still goes along with his personality. The idea that the anime used to portray his fall was that he couldn't handle that the world was so cruel to let so many others fall to darkness. This goes along with his general portrayal as seen throughout the series where Alibaba does cares deeply about other people. This can be seen as early as the first arc wherein Alibaba decides to save the child who falls into the desert hyacinth despite his previous arrangement with Budel. There are numerous other examples of how Alibaba cares for others, even if they aren't directly affiliated with them throughout the series. The anime only addition simply helped give a seemingly large climax for the series that would have otherwise been underwhelming considering it was the final arc of an anime that may or may not have gotten a sequel.
Source: Reddit : Magi : Anime and Manga differences
Related: Differences between anime and manga versions of Magi: The Labyrinth of Magic