So anybody still arguing for the inherent superirority of analog may be justifiably labeled an ‘audiod’, I suppose.
Would this work? Prepare an audio CD and a vinyl LP with a sequence of single tone recordings-cover the whole audio range (30 Hz-18,000 Hz). Play both with the same speakers, and analyze them both with a spectrum analyzer. That should answer any questions.
Not really. Frequency response is only a part of the equation. You also have to take into account impulse response, distortion levels, stereo field (as has been pointed out, vinyl cannot play back out of phase signals in low frequencies) and other such things. Everybody except die-hard woo audiophiles already agrees that digital is objectively more exact, but that’s not what most of the discussion is about, anyway. It’s about perceived sound, haptics and nostalgia, not a small part of anyone’s enjoyment of music.
24 fps film is better. Random grain patterns. There is no audio equivalent.
Minor hijack - I follow these types of discussions when they appear, but rarely post. They happen all the time on guitar message boards - there’s one on the Acoustic Guitar Forum that had legs for a couple of weeks asking “why aren’t more questions about guitar tonality answered with a spectrum analyzer?” And we could go a ways discussing tube guitar amps and old analog recording gear, both of which are a big deal as tools for some musicians.
I find that the lines drawn during these discussions are helpful in exploring the detail, but whenever folks take a Big Stand on these types of topics, they are likely talking past each other.
Is digital a hugely more powerful recording and playback process vs analog? Of course. Was early digital funky-sounding due to inadequate remastering, weird, flattening compression algorithms, the emergence of small, tinnier earbuds that built on the convenience of digital music, etc? To me, yes - many mp3 files sound awful, especially when played through cheap-ass earbuds or through laptop speakers.
By the same token, vinyl/turntable/old school audio geekery - something I don’t do at all - do I get that it “elevates” the act of listening to music? If you have to set aside time and throw more coals in the boiler to fire up the steam-powered turntable 
it is more likely that you are looking to get something out of that music experience that is different from tossing an iPod into your bag to have for your morning commute? I can see that it is.
So I have issues with twits who want to argue how “analog is superior” - but I have no issues with folks who love their vinyl/analog music for what it does for them, if that makes sense.
Grain is a flaw that can be easily simulated in digital imaging. Filters to add and match grain are standard in most tools. I think that’s a case of taking imperfection as representing “better,” which it might in some esthetic sense, but it does represent inferior reproduction.
I’d put forth that acetate and tape noise are equivalent audio phenomena.
The key thing to remember when arguing about digital signals is that (1) the signal quality doesn’t matter at all as long as most of it gets through because (2) all digital signals use error-correction. As much as 50% of the signals from CDs, DVDs etc. are error-correcting information.
(I know you probably know that, but I thought I’d throw it out here. It’s not just that digital signals are somehow magically immune to transmission flaws… they ARE immune to a certain degree of transmission flaws.)
What about vinyl record degradation? Even the lightest, best balanced tonearm exerts a downward force on the needle-and wears away at the grooves. Can audiophiles actually detect the difference between the initial play and the 20th play?
Finally-are high quality cartridges still made? The market must be small, indeed.