Should All Power Cables be Alike?

This has been very helpful. I'm certain they put 12awg in the wall. I have 20amp circuit breakers. The manufacturer's owner manual for my power amp indicates that the AC should be connected directly to the wall outlet; not passing through my PS Audio P10. Is that the optimal sound quality approach?

Many members find that to be the case. I hate to keep saying this, but the only way to be sure is to try. I personally have not tried going directly into the wall, but that's because I don't have enough outlets at the wall because I have monoblocks. I plan on installing a dedicated line (right now there are 3 other outlets around the room on the same branch) and another outlet where it comes into the room. Then I'll be trying and deciding for myself as well.
What amp do you have?

So, you recommend using a 10 or 12 gauge AC power cord - I assume that translates into a 20 AMP AC cord from the AC wall outlet to the power center? I have 20 AMP AC wire to my circuit breaker.

The circuit breaker and dedicated line are rated 20 amps. Your PS Audio is 15 amps, so the wall receptacle would be a grounded 15 amp type. A 20 amp receptacle has different connectors.

I ownhigh end power cords ! End to end would encompass the world!! Cardas 1000.00 Clear  to Shunyata to Wireworld platinum power, and the beat goes on! Can power cords change sonic capabilities of electronics! Yes, they can! Is the incremental improvement worth the money! NO, it's not! 
Before you bear fangs and head for my throat, my statement is in my opinion! I have just short of 100k invested in a high end audio system! .Power cables won't change modest priced equipment into mega high end audio 

@lowrider57 good point, I missed that. 20 amp power cords have different connectors at the component end and will not fit on components with 15 amp IEC inlets. Most components have 15 amp IECs. The plug and connector ratings apply mostly to which IEC and outlet they'll work with. The current handling rating mostly comes into play when taking the gauge of the conductor into account. So a 12 or 10 gauge power cable could safely carry 20 amps of current. But you don't want to get a cord with 20 amp connectors because it won't fit into the back of your amp..