There is no real wrong answer on this as long as you don't go overboard and still feed a "balanced" ration. Layer typically has 16% protein. Grower typically has 16% protein. The only significant difference is the calcium. The Flock Raiser I see is 20% protein. Any of them are fine. My standard when I don't feed Layer is Grower when I can get it, and Flock Raiser when I can't. I always offer oyster shell on the side regardless of what I feed, even when I feed Layer.
Protein is not the only issue. They also need fats, fiber, minerals, vitamins, and different amino acids. Corn, like any other grain, provides many nutrients, but it does not contain all the nutrients in the balance they need. If they free range, they will balance it a bit for themselves, but even with them free ranging I try to not feed a whole lot of any one thing, whether that is a grain, greens, or any one specific garden or kitchen waste.
They can generate heat from anything they eat, even protein. Some things obviously are higher in calories than others. As long as you are feeding a fairly balanced diet, they will manage quite well. I really think a lot of the special things many people do for their chickens are for the people's benefit rather than the chickens. Chickens are pretty adaptable as far as feed and can still do well with all this special treatment as long as they get a fairly balanced diet. But that is just my personal opinion, no real science to back it up.