Personally, I think the writing has improved tenfold over the first game. I didn't find the 'darker' tone to be in any way forced or leaden. It's handled with confidence, and I feel the writers know what they're doing. Talking rats and whatnot are quirky enough for me without being nauseatingly corny.
I didn't like the first game's writing at all - there was far too much sugary sweet, tongue-in-cheek, winky-wink goofery for me to stomach. It wasn't horrendous by any means, but its plot was hyperactive, and its characters paper-thin.
By contrast, I found the first section of D:OS2 highly memorable. The shriekers are particularly creepy bastards, and I like the ambiguous morality of both the protagonists and the antagonists - I never felt I was playing a stock 'good guy', or that I was opposing homogeneously villainous enemies. Overall, a good start!
The only problems I noted related to the goofier historical baggage from the first game, shoehorned into a maturer story. The name Braccus Rex, for example, always raised a chuckle for me. It's screwball and parody-ish, especially the 'Rex' part. Like he was meant as some lampoon of the standard dark lord type. Here the character is given notable depth. He has a presence everywhere you go, and comes off as an enigmatic badass with a textured history.
Then you read some random character mentioning the 'Rex' part again, and you recall the black-armoured juggernaut with the flaming skull for a head that you meet down in some dungeon during the first game, and somehow it kinda falls apart...
