Well, first, there's streaming, and then there's streaming. The first could be "local" streaming, from a NAS for instance. Second could be "internet music service" streaming, like Qobuz or Tidal. I think they're similar enough they can be lumped together. Some might disagree, but I think playing off a networked music streamer/player with internal hard drives is also close enough to put in that group.
My opinion is that you have much greater potential with any of the above, than with CDs. Spinning, mechanical platters are removed from the equation, as are plastic discs that erode or get damaged with time and handling. Also, with a CD you're limited to that particular recording, where with streaming services you can potentially choose among multiple recordings, including many at higher resolution bit/sample rate.
As to comparing hi-res files played (I'd argue, "streamed") from your Aurender vs hi-res files played from an internet music service, it will be hard to tell the difference. It's not until I play DSD files from my local NAS do I start to hear a difference to hi-res streams from Qobuz. Even then, DSD are not always better, just "often".