The Knights of the Nine questline is for good characters. The Dark Brotherhood is for evil character. So they are incompatible.
In my opinion, the Dark Brotherhood questline is worth doing at least once. More than once might be boring, but it's good the first play through, I think. Still I would start a new character for the Dark Brotherhood, since they are evil and a noble and virtuous character that completed the Knights of the Nine would not do that questline, in my opinion.
That's how I see it, too. I put off doing the Dark Brotherhood, because I never managed to come up with a character that would do those things, and whom I liked well enough to want to play. I've finally come up with a character I can believe in, who is doing the DB quest line.
I can see the possibility of "redemption" in a character. If one started out as an evil character, one could do the DB, Thieves Guild, SI (which is morally ambiguous, at least), and the darker Daedric quests. One could then "find religion," and start KOTN. The other way around is very hard to fathom; a noble Knight of the Nine is not interested in being a murderer or thief.