My CD / DAC and Streamer / DAC sound the same when playing the same red book files… from CD (I am using the same DAC I either scenario), stored files or streamed. This is true for me by design… getting the highest quality sound at my level of investment. However, streaming sounds better when streaming high resolution files like the half a million albums on Qobuz.
I am not completely sure at how you are looking at the CD comparison. what a CD sounds like is dependent on the transport and DAC. I am going to use cost as a shorthand for performance. So for instance if you were to compare my streamer to say a $5K CD transport (with the same DAC being used) or $10K+ CD player, my streamer would sound much better, as well as having far greater functionality.
A streamer can easily sound much better than a CD player or transport. It depends on the comparison. The sound of a CD is fundamentally controlled by the equipment used to play it… as is streaming. The better the player / transport or streamer the better the sound.
Sorry if that is either over explaining or a bit jumbled. I’m just not feeling very concise at the moment.