I can't tell any difference between leeks I havested earlier when they were thinner, and later ones when they had fatterned up, so I would say the fatter the better.
All my leeks stood well during the winter, both thin and fat, but I am in the south and on a heavy soil.
Never tried them as mini leeks, about the size when you plant them out to their final spacing, maybe I should try a few this year instead of giving my spares away.