LPs - since their introduction in the 80's, I have heard thousands of CDs on hundreds of systems, including many > $100,000 systems. So far, only one of these systems has matched the quality that I hear from my mid-priced analogue system. I estimate that the aforementioned system exceeded $200k, MSRP.
That being said, I also have hundreds of CDs and a 'class-A' player. I usually play CDs when I need a longer hands-off period of time. For example, if I am cooking outside on the back deck, but still want some background music during the prep and eating diner, CDs are a better choice.
You may want to search the dozens of prior threads that asked a similar question...