|Koi eat a lot, Goldfish do too, but Goldfish are better foragers.
If you took two identical ponds and you neglected to feed both ponds equally, the population in the Koi pond would die out faster than the population in the Goldfish pond. Part of the reason is that Koi eat more, so they starve faster. Part of the reason is that Goldfish will find food anywhere, including swimming prey like rotifers, fish fry and insect larva. Koi on the other hand tend not to identify or attack small prey like that. Their usual foraging method is bottom sifting. And if the pond has no aggregate or mud on the bottom, there will be no natural forage.
I think most people would be very surprised by the amazing amount of live, squishy and crunchy food that can be found living in the gravel of a properly maintained pond. Sometime if you're ever bored, siphon thirty gallons of water out of that gravel and put it in a plastic sweater box. Let the sediments settle and then look at the writhing life making tracks in the settled sediments. That's Koi food, friends.