Many people even including top competitive programmers do CP on both Codeforces and Codechef. I want to know there experience on both sites in terms of the quality of the problems they faced.
A lot has been answered in past, I will try my best to not to re-iterate those points.
One of the differences is, codechef holds both long and short contests. There is a difference in problems for both of them. In short contests, setters have to make sure that the set is solvable within the decided time - so try that coding and writing part is not very huge. In long contest, anything can happen :). The more mix of ideas, the tougher the problem.
Codeforces contests are exciting - in the sense, they are so competitive. Every second makes a difference in ranking with the score drainage, and there is a pressure of testing your code and “AC-in-one-go” concept (else you might fail systest and get a 0!). Contests at codechef are a little chilled out.
I think CF has a lot of problems, especially on maths and data structures like segment tree. But there are a few topics which are “rare” on CF. Like, I think I dont see as many problems on generating functions on CF as I see on CC (not to mention its a pain to find them on CF under “Math” tag.").
Quality of problems on both sites are good- you just have to make sure you take the best of both worlds. I feel CC problems are more oriented towards learning (because a good bulk of them come from long contests) while CF are more oriented to exploring various implementations and optimizations of the same algorithm.
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