I read the translated Trigun manga over the weekend, and my reaction to the material despite being a fan of the anime made me realize that the books are not always better than the TV show or movie adaptations. Several popular series are actually expanded on and filled out in their TV versions, adding depth and characterization.
The biggest examples I can think of are Marmalade Boy and Magic Knight Rayearth, two popular anime series of the 1990s. The Marmalade Boy manga was only 8 volumes, but it spawned a 76 episode animated series. Many of the additions deepened the storyline and helped the main characters grow. Magic Knight Rayearth was 2 3 volume manga series, but it was converted into a 49 episode anime. Fans of MKR often credit the anime with fixing some of the plot errors present in the manga and being more enjoyable.
Even fan favourite, Sailor Moon, is only an 18 volume manga, which provides the bare bones for the 5 season anime series, 3 animated movies, several live action TV series, and even musicals. Most fans found their love for the series through the anime because it fleshes out a lot of the background stories only hinted at in the source material.
What adaptations have you seen that you think are better than the original works?