For me, it was the theme of child abuse that most of those other shows don't have(I haven't seen Now and than, Here and There) that made Monster really rough to sit through at times. The whole thing about the 511 Kinderheim was brutal and as others have said, the fact the show is fairly grounded makes it far worse because it feels based in real life atrocities, if not actually based in such.Despite how draining it can be. Monster is more up beat than shows like Black Lagoon, Desert Punk, Now and Than, Here and There, Elfen Lied, and some other depressing anime I can't think of at the moment.
Black Lagoon had rough spots too but the fact a lot of it is over the top kind of overshadows stuff like "Hansel and Gretel" which is the closest that show gets gets to true bleakness. Elfen Lied all I remember is the infamous Puppy Scene, which felt calculated to make Lucy evil and then justify the murder spree.