Another factor is what kind of components you are talking about. Some are less susceptible to power cord changes. What kind of CDP and amp do you have?
When I used my Pass xa30.5 and Modwright Oppo 83, I found the Oppo to sound better when I used a better power cable on it.
For critical listening I find two approaches that work best for me:
1. Choose a well recorded song you are very familiar with and only play a short portion of the song which highlight some key area like bass, piano and vocals. Maybe for 30 sec to 1 minute worth. If it is too long then it clouds things. You can even right down how you think it sounds. Then switch cables and try it again. You are doing to have to go back and for a few times with this until you can hear the difference.
2. The other way is to leave it in there for 2-3 weeks and to just listen casually and see which one you enjoy more.