The benefit to CNN is that almost every household had/has access to CNN. It's some channel on basic cable, even if you didn't regularly watch it, it was easy to find and was pushing the same news out to everyone.
Twitter on the other hand is not as simple to just start using. You need to sign up, and then find the right people to follow (granted, Twitter does try to make this easier), but for any given event it's hard to find in real time a tweetstream that is going to be better than just watching CNN or other major news outlet. On top of that, Twitter is filled with parody accounts, people making stuff up, and lots of other noise.