To my delight, this has not become another 'war'.
My call is that it depends on the individual LP or CD, as well as the gear it's being played on. Some recordings are simply better than others; Some discs (LP or CD) are produced better than others.
One common fallacy I've seen is the 'vinyl junkie' who's spent tens of thousands on his analog rig and is comparing it to his $900 CDP. There's some self-fulfilling prophecy for you.
For whoever asked, TTs, tone-arms, carts and the media itself have all improved, so new LPs on a nice rig can be quieter. That being said, digital media still DO have better dynamic range AND frequency range. (And if you're not listening to pop, you can mostly avoid the 'loudness war' compression.)
BTW, if you think you like 33-1/3 rpm LPs, try listening to a 45 rpm re-issue of some favorite recording. After that, it's hard not to see 33-1/3 as anything but a huge sonic compromise.
I'm surprised that nobody has mentioned SACD (DSD), or maybe I missed it. In my experience, DSD is the best of both worlds. IMHO, SACD is to CD what 45 rpm LP is to 33-1/3.
But once again, it is the individual recording & production of the media that always makes the biggest difference, so there's lots of overlap.