We can rule out beef immediately, because it's so rare in pre-1.9 worlds. This leaves wheat and melon.
I personally prefer melon. In my experience, I have noticed that an individual melon grows more quickly than an individual wheat plant, once the stalk is grown. Melon is remarkably easy to harvest, you don't have to replant it. You just have to till the ground under the melon with a hoe. It is more efficient than bread in certain ways as well; three melon slices restore three hunger points, and three wheat (one piece of bread) restore two and a half hunger points.
Bread has two distinct advantages: you can store more in a single stack, and it also provides saturation points.
You can counteract this my carrying a stack of melons instead, and placing and breaking one whenever you need food. Each melon drops 3-7 melon slices, so that averages five slices per melon broken. By those numbers,
64 melons = 320 hunger points
Therefore, I believe melon to be the more efficient food.
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Chicken. Set up an egg farm and throw the eggs at a wall. Then you get xp for killing them. Melons are good because you can eat with one food bar empty and not waste food.
For 1.9 breeding cows would be good because that gives you leather, but it takes a little more work.
Actually if you obtain it in extremely obnoxious quantities it may work. Seeing how it is not a 100% poisoning chance (I'd say about 80) if you ate extreme amounts of it at once, you could over come the poison and regain your hunger .