For working around my Snapshot world's island base I prefer carrots. For expeditions (particularly those to the Nether) I take baked potatoes. Though I eat all the minecraft foods. It doesn't really matter what you eat but the the choices are fun.
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Under no circumstances do I want villagers building ugly little houses in my world. That's my job.
Baked Potato: Food 6, Saturation 7.2, Effective Gain 13.2 each, Total gain per stack = 844.8
Carrot: Food 4, Saturation 4.8, Effective Gain 8.8 each, Total gain per stack = 563.2
Both Baked Potatos and Carrot have the exact same food:saturation ratio.
Potato is the clear winner for me. I don't care about furnacing time because I can have that happening back at home where I am safe and doing other things while it bakes. The less eating time the better. The longer a stack of food can sustain me for the better. And when used in combat situations for topups the more saturation, the longer before I have to eat again to maintain health regeneration.
They are both balanced (in my perspective at least).
Potatoes recover more hunger bar units (if baked), but carrots have more uses.
But it doesn't matter for me, since I will build huge farms to collect huge quantities of both.
However, if I were to choose one, then it would be carrots, since I can use it for different stuff e.g. brewing.
Ideally, I like having both and being able to eat both. I actually like the idea of poisonous potatoes because in reality, raw potatoes can be poisonous if eaten. Carrots take your body more energy to chomp on so the 1 Drumstick healing makes a lot of sense, too.
On the other hand, I, too, agree with the stew option and I also wouldn't mind a 'salad' option of carrots and apples.