The first question you have to ask is "Am I comparing the same masters?" Most often, if you have an older CD, then NO, you are hearing a newer master from the streaming service, and it's usually not better than what is encoded onto your CD.
I have compared some CDs to the album on Tidal, and found them to be identical... but MANY times, the streamed version is louder and more compressed, and therefore worse sounding. Sometimes the difference is subtle, sometimes dramatic, but I have heard a few sound nearly identical. So that tells me the streamer CAN indeed match the sound of my CD player (an OPPO 105).