The low voltage side of a transformer needs to handle more current. You could use the same gauge on both sides and get the same voltage, but you'd experience more losses.
if you used the thin wire on both sides you'd get the same voltage but experience more losses
if you used the thick wire on both sides you'd get the same voltage but have a much heavier and more expensive transformer for an almost undetectable performance improvement
if you used the thick wire on both sides you'd get the same voltage but have a much heavier and more expensive transformer for an almost undetectable performance improvement