Nickelodeon's problems are that it has some really dumb shows (like you said) and it puts way too much emphasis on cute, non-violent, happy-go-lucky shows like Rugrats and Rocket Power. And TeenNick is not at all more mature or anything, it just has a lot of extreme physical comedy, like pie-in-the-face, etc.
Cartoon Network is very enterprising, and constantly has opportunities for new shows to show up. In the summer, they let you choose what show would be developed as the newest Cartoon Cartoon, and their shows are not the usual "kid makes mistake, kid messes up, kid apologizes to parents" kind of thing like Nickelodeon.
Another thing is that while Disney and Nickelodeon have special shows for toddlers, Cartoon Network has Looney Toons, which can be watched by people of all ages.
And, of course, Cartoon Network has shows for non-kids, namely, Toonami and Adult Swim.
There's something about really funny cartoons that people prefer over cheap comedies, age old sitcoms, babyish shows, and whatnot. That's why Cartoon Network is so successful.