Elfen Lied is really not gory in my standards haha.
Yeah for Air Gear the Manga is way better (well like most of the anime series that came from a manga root.) Same for Gantz, the manga is still kick ass, Hellsing too and shitload of other anime get their ass kicked by their manga origins.
So for animes I can't help you, but in manga yes. If you like what you see with Monster, you can look out for 20th Century Boy, it's from the same dude. Awesome Manga, really intelligent, and good cast of characther, it's set in the 21century, and it's the story of a gang of childhood friends that wrote a book where a robot would attack the world and they would save the world, when they reach their Adulthood, someone took the book and build the robot. So you follow them as they take on mysterious persona called Friend as he try to dominate the world.
Battle Royal if you like gory manga is awesome, it's gore on the visual side, and on the psychologic side too. Another manga that's way better than is other media (the movie, well I could say that the Book is as good as the manga, it's almost the same only more illustrated and with 2-3 chracther added to do more sense, actually, the new characthers actually help with some flaws of the book.)