Are chest fridges more energy efficient?

Obviously, lots of variables are at play, but say I have two fridges that are identical apart from the fact that one is upright and the second one is a chest fridge. And obviously you can't just lay the upright fridge on its back because of the compressor, so it's one that's designed for it. When I open an upright fridge, some of the heavier cold air will fall down and will be displaced with warmer air, therefore, the more I open an upright fridge, the more it has to work to keep itself cold. But with a chest fridge, nothing is displaced, because the cold air lies on the floor already. Am I making any sense?