A dedicated line is what matters most, in my experience, with a good power cord as number two. I use Synergistic Research A/C Master Coupler X2 for my Atma-sphere Ma-1 amps. No miracle but they do sound better than stock cable.
I think that, the better the line to the amp(s), the greater the difference between power cords, good, medium and bad. But I am not sure if this is a rule. At least, both play a role.
This is built on long term experience with Krell FPB600, Atma-sphere MA-1, and other amps. I experiment with power cords but get to a point where I think, "good enough". This is the case with my Synergistic, Shunyata and Wywires cords, while others, like my Supra, is more so-so.
The greatest change, for me, was with a dedicated line. This was almost a revolution, with the big Krell. Much more authority, better bass, imaging, etc. I was amazed. The advantage is clear also with the MA-1 amps.
