Do I need 10 gauge power cord if I have 10 gauge from panel?

I think Nelson Pass said this although not sure it was his quote originally: "Some of what we can hear cannot be measured & some of what we can measure cannot be heard". Sound reproduction is not an exact science because there are simply too many factors involved, especially the unpredictable interactions / compatibility between various system's components. 

Just listen & see what you enjoy the most. It doesn't matter what anyone thinks or says. 

OP,

Only when comparing to other cords. This is not a pursuit with absolutes… maybe the desire, but we live in a world of imperfection.

No.  There is no reason to match.  After all, do you know the gauge of the power line coming from the generating station to your home?   Miles of it.

Just make sure it's heavy enough to comfortably carry the power being drawn by your amps, which figure will be published by the manufacturer.  My uprated Krell KRS200s can draw up to 1.8kW per side.  I use the UK equivalent of 12 gauge from the board and the standard cord supplied by Krell, who may be presumed to know what is required.

No, you do not.