The general theory is the heavier the gauge the better. It's simple Ohm's law in effect in this case. The less resistance from the cable, the more power goes to the speakers.
There is no magic between the $1,000/ft. cable vs. the $3/ft. cable. There may be some trivial effect in an OFC (oxygen free cable), but in my opinion, it's not worth the extra money. A conductor must behave as per Ohms' law, no exceptions.
I also don't believe that some cable companies claim that theirs is superior because they overcame the "skin effect" by using flat cable. Nonsense! Skin effect is so trivial at audio frequencies that it's meaningless. Most of the skin effect takes place in the megahertz and gigahertz frequency ranges.
To show my point, look at the size of the wire from the output transformer (or output transistor) from the inside, going to the back of the amp's speaker connector. Most are not larger than 10 gauge, typically if a transformer, about 16 gauge. Then look at the wire inside the speaker going from the connector to the crossover and then to the voice coil. Most wires going to the voice coil are 18 to 20 gauge!
The length of wire going from your amp to the speaker has a finite resistance which has an effect on the delivery of the power. I never understood how a piece of wire can affect the sound of the music. I tried many and never heard any differences. Remember the fairy tale about "The Emperor's New Clothes"?
