It really depends on the specific animal, but common wisdom is that you can't just leave a bowl of food out for a dog. Cats on the other hand often are free-feeders (leave out a big bowl of food and refill it on a schedule). Of our 2 cats, one will eat until she vomits and one will barely touch food if it's out at the wrong time.

It depends a lot on the dog— what I've seen with dogs is similar to what you describe with your cats.

There are 4 dogs in my house, one belonging to me and three belonging to my roommate.

Mine won't really overeat unless she's offered a lot of something extremely appealing (like human food). At least 2 of my roommate's dogs will eat until they make themselves sick, though. The last one, I'm not sure.

This is going to depend on all sorts of things, especially how the animal was raised from a bit.

In the dozens of cats and dogs we've owned over the decades, we've always kept bowls out for them stocked with food.

What I often hear from friends when they discover this is that they'll try to move from their scheduled feeding to free feeding, realize their animal is engorging itself, and then assert "see? doesn't work" or "nope, {cats,dogs} can't do that."

My anecdotal experience agrees with this assessment. My family has always been free feeders and it hasn't been a problem for our dogs.

I've had 7 cats at various times in my life and of those only one would eat too much if food was always available.

Cats overeating is 100% genetic. I've raised 12 cats in my life, all fed the same way. Only 2 ever got fat.