I think this is a 3-horse race, not a 2-horse race:
CD
locally streamed files from a hard drive or NAS
files streamed from a service
IMHO the last two aren't the same quality, and without knowing the details about the streamed masters, it's hard to even know if you're comparing apples/apples.
IME, on locally streamed rips vs. the same CDs, the files always sounded better. Ripped SACDs vs. the same SACD, same result, the files win. YMMV. Cheers,
Spencer