The monster-anime is great. Dunno about the manga, but I would assume it's great as well. (usually the way it goes with good animes, great manga!)
However, Monster does have a few points that I find are annoying.Spoiler!
What I enjoy most about Monster is probably that all characters in the anime at least go through development, which I find is pretty rare in at least animes nowadays, the protagonist usually goes through some changes, but the sidekicks remain in the same mental state all the way through.