Are you sure the difference isn't just the DAC inside of the CD player vs. whatever DAC you use for streaming?
I have a Primare CD32 that I connect to a Topping D90SE DAC via toslink because I think the Topping DAC is better than whatever is in the CD32. I also connect my Laptop directly to the Topping D90SE via USB and output the sound to the same amp and headphones.
This way, I'm really doing a direct comparison between what is essentially a CD transport, and Qobuz. And honestly, the difference is so small I can't tell if it's just placebo. I feel like CD is maybe slightly more dynamic and has more bass, but that could be just wishful thinking, because I'm talking a like 1-2% difference.