It does make a difference although not perhaps in the way cable companies may advertise. Generally a heavier gauge power cable will provide a better perceived response than a smaller gauge in a power amplifier with a higher power demand. You can buy 12ga power cords at Home Depot and terminate the amplifier side with a proper three prong socket- if you know what you're doing, and wind up with satisfactory results. I have and I did.
Almost all new amplifiers use solid state rectifiers that allow electricity through in bursts so even if your power consumption is 400 watts as a steady state, in the moments power is pulled to charge the power supply caps it may be drawing much more. A heavier wire will deal with this better than a lower gauge wire which is why appliances spec an amperage rating, as do power cables.
Almost all new amplifiers use solid state rectifiers that allow electricity through in bursts so even if your power consumption is 400 watts as a steady state, in the moments power is pulled to charge the power supply caps it may be drawing much more. A heavier wire will deal with this better than a lower gauge wire which is why appliances spec an amperage rating, as do power cables.