The sound I get from playing 58 year old albums on my 38 year old turntable is much better than the sound out of the CD player.
I guess you're not bothered by the noise

Personally, I could live with the constant low-level noise... if I had to... But the occasional nasty clicks & pops always annoyed me, even in the analog days when it didn't seem to bother most people.
Vinyl also has frequency response variations, both in the record and phono cartridge. Most of the old rock records I used to listen to had rolled-off highs and I was always foolishly upgrading or wanting to upgrade the cartridge instead if simply turning-up the treble. I think I was reading too many hi-fi magazines and I felt like my setup was inadequate or that I was "cheating". But I
knew the real problem was the records because there were some good-sounding ones.
And you get occasional audible tracking distortion on some tracks.
CD players do have a "different" sound (S/N Ratio/Dynamic Range)
The
sound of the dynamic range ("dynamic contrast") comes from the
recording. Records are sometimes better than the digital, especially if the digital is "loudness war" remastered to be constantly-loud and louder than everybody else. (There was a loudness war in the analog days but they didn't have the modern digital "weapons".)
The dynamic range
capability of CDs is around 96dB and you're lucky if you can get 60dB from a record. It's limited by noise on the quiet-end. You can ALWAYS hear background noise between tracks on a record and sometimes during quiet parts. Digital has quantization noise which you can hear at 8-bits but not at 16-bits or better (under normal listening conditions).
There can be noise from the analog-side of the DAC in a CD player and some are better than others, but it's rarely audible.