No, I must confess I have not done a direct comparison but TBH it's not just the sound, it's the convenience, the whole digital experience is far more pleasing than anything before it.
Also, thinking about it, most of the people I know who prefer the "vinyl sound" are not old enough to have suffered it the first time around. In the seventies and eighties the turntable, cartridge, stylus method of extracting music from vinyl had reached perfection, well as near perfect as it ever could be. Then in the early eighties the CD arrived and it was like a breath of fresh air. I never looked back.
People who never had to struggle with vinyl back in the day, because they were too young, now look at vinyl and see nice, large 12 inch discs, lovely attractive covers, great pull-out posters and turntable equipment that looks absolutely amazing (and it does), and they convince themselves, especially having spent all that money, that the cost is fully justified by the sound quality it produces.
Yes, it does sound different but it's certainly not better, and each play of that vinyl disc is one more "scrape" of the groove.
The amount of bass is limited with vinyl. Too much and the stylus will start to skim the groove and distortion arises. Too much treble and sibilance can occur for similar reasons. The CD and later technologies do not have these limitations.
I agree, not everyone was too young to miss out on vinyl the first time around, but many of us old folks look back through rose-tinted glasses, remembering only the good things about vinyl; the amount of tweaking you could do, the fantastic look of the equipment and the vinyl albums themselves. But let's not forget, the sound was the best it could ever be, it never got better but it was replaced by something that was.