I'll agree that Wolf Among Us doesn't stay 100% true to Bigby's character but I wouldn't call the narrative told to be dreadful. If you're going through the genre you're basically there for the ride / story. My biggest quip is that the "choices" you're given don't actually affect anything. But that seems to be a common theme in TellTale games.
I didn't really hate The Wolf Among Us. It got me interested in reading Fables. But Fables is waaaaay better, where I find the Walking Dead games to be better than the (still very good) comics.
This is to compare the story to Heavy Rain, where decisions and missed actions do actually change the story in some way. The play-through can be changed where Wolf and, say, Walking Dead are fixed.
But the thing about Season 1 is that it's not about "what you change" like you're the stereotype game character demi-god. It's about WHO you are in the post-apocalypse. It offered a morality play that transcended the trite and typical "be all bad or all good and get rewarded for either choice". One of my fondest moments in gaming is during the cannibal episode. I brutally killed the first brother, because I fucking hated him. But I felt really bad when I realized that Clementine had seen this. So I actually spared the next guy. Sometimes I acted out of self interest or survival, but it, and my bond with Clementine, made me interested enough in trying to redeem myself.
Seasons 2 is even more limited, but that's ok as I feel it's thematically more about the heat death of the universe. Not who the characters are, after all, Clementine is firmly established at that point (though my Clementine was not always a good kid because my Lee was not always a good role model), but how to carry on living at all with the slow dwindling of supplies, morale, people, and even the temperature. You can see this plot thread repeated multiple times through other characters in the story. It was very fascinating to me, so it got a pass.
Wolf Among Us was, ehhh, I guess it leaned a lot on its source material only to not really live up to it. You do just get kind of pulled around and don't get to really solve the mystery yourself because that would change the game too much.