I am not, at all, a fan of vinyl. It's expensive, I have no interest in fussing with turntable setup, and I find the noise and all of the other issues inherent to the medium irritating. I have collected vinyl in the past and understand why people enjoy it, but I long ago stopped myself.
THAT SAID, I do think it's undeniable that vinyl playback can frequently sound more pleasing than digital, if you are just focusing on the the tonality of the music and ignoring the noise and limited dynamic range. I think this can be particularly true in the context of, say, a serious vinyl enthusiast who cares about their equipment but isn't necessarily a full-on audiophile dork obsessed with EQ and speaker performance and all that. I'm hard-pressed to tell people like this that they're wrong when they say vinyl sounds better on their system than the same music played on Spotify. In many cases, I've heard it side-by-side on their gear and would tend to agree.
The most identifiable and generalizable character that vinyl has, to me, is that it tends to be warmer and punchier in the bass than digital music. This seems to defy the technical limitations of the medium in the lower frequencies.
My theory is that this may be due to the summing of bass frequencies in vinyl masters, and - crucially - that this tends to sound better on the typical stereo system.
Take my own system, for example. My mains are relatively bass-limited two-way speakers. I have two subwoofers (well, actually eight subwoofers split into stacks of four) that flank the mains, with the crossover implemented with DSP. When I run the subwoofers as two separate channels, each getting the left or right bass frequencies, it does not sound good. The bass is very anemic and it seems to exacerbate all of my room issues. On the other hand, when I run the subwoofers as a single channel getting the summed bass frequencies from the left and right channels, it sounds fantastic.
A person whose system consists of full-range speakers in stereo, with no fancy DSP, has no such ability to sum the bass frequencies and is stuck with the bass as-mastered. If the vinyl master has summed bass frequencies while the digital master does not, then it's easy for me to see how the vinyl could be perceived to have superior bass and an overall warmer tonal balance. What I don't know is how mastering engineers approach mixing bass frequencies for digital masters - is it common to mix them in mono or are they more often left in stereo? I imagine this is also genre-specific, e.g., I'm sure much electronic music has bass in mono whereas more acoustic music may have a wider stereo mix.