There will be many replies to your question. Some very smart individuals with electrical engineering backgrounds will make compelling arguments in favor of using the same gauge wire in power cords as that which is in your walls because from an engineering standpoint it makes sense to do so. It will be very difficult if not impossible to fault their position.
That said, to my ears, I hear a noticeable improvement using 10 gauge (or larger) power cords on my amplifiers. I can't explain why it is. Perhaps it a placebo effect. Nonetheless, I continue to hear a difference, and therefore I buy larger gauge power cords. I do not hear an appreciable difference using a larger gauge power cord on sources.
That said, to my ears, I hear a noticeable improvement using 10 gauge (or larger) power cords on my amplifiers. I can't explain why it is. Perhaps it a placebo effect. Nonetheless, I continue to hear a difference, and therefore I buy larger gauge power cords. I do not hear an appreciable difference using a larger gauge power cord on sources.