Finished Urasawa's dramatic manga Monster! a few days ago.
If one isn't familiar with some of the conventions of manga, reading this you'll find a fair amount of over-emoting and a lot of drama-injection over ultimately small plot points, but this mostly owes to the episodic nature of the material. Like most manga this was released bi-weekly for years, and when you read it in collected volumes (tankoubon) like this it compresses the dramatic scenes together and their frequency amps up into melodrama territory.
Nonetheless, this is a first-rate dramatic story. Apart from the above caveat, other scenes (and the emotions therein) are handled with deft subtlety. Urasawa's artwork is a real grower. You'd think at first glance it was just sort of workmanlike, but as the story moves along you realise how talented the guy really is. There's a huge cast for the type of story it is, and his ability to keep everyone distinct and well-characterised with both art and writing is pretty admirable. His talent also shows how a topic normally consigned to film or television really can make a good manga... a medium characterised by the phrase over-the-top.
The last few volumes really dovetail everything together well. In the final book I actually found myself getting a bit choked up in two or three places, and the last revelation to the reader, though it wouldn't seem like such a big deal out of context, was pretty devastating from within the story.
In some ways you get a lot out of it that you might've from Death Note, but more believable (of course) and without any supernatural aspects... though the villain, Johan, is inhumanly evil.
At any rate, take a break from robots, battlesuits, and lolis and give Monster! a go.