As said earlier, Boku dake ga inai machi (Erased) is an interesting case.
The anime has a way better artstyle, really awesome VAs and OP/ED and even adds a few good scenes. But in the other hand, it skips other important scenes or informations and really changes the end of the story (and not really in a good way IMO).
An anime I liked is Gantz, I think it's really good compared to the manga, mainly because it's great to see everything in action (even if the anime ended with only one season and a not great alternative ending).







