I read somewhere that the writers rooms of Daily Show and Colbert rarely cross, at least day to day. I believe they deliberately keep them separate to keep them tonally unique, even though it sometimes results in both shows covering the same topic, and even occasionally making the same joke.
I did some UX consulting for The Colbert Report that required me to research their entire writing and production workflow and my understanding is that the executive producers of the shows might check in with each other, but it's true that there's essentially no overlap, and there's no effort to coordinate topics.
(Sorry for no source on that.)