For one thing, because a vinyl record is analog and not digital, it is not missing information. An mp3 is a lossy format; it samples pieces of the music but does not capture it all. A good quality mp3 (192kps or above, 320kps if you have superduper ears) will sound pretty good, and your brain will not hear the missing pieces of music, instead it creates a bridge between them so that it thinks you are hearing everything. A low quality mp3 (32kps or 64kps) will have even more information missing, and will be noticeable to the ear, usually sounding very tinny and hissy with 'gurgly' vocals.
There is no 'scientific proof' that vinyl sounds better than a CD; that would be a value judgement that can't be proven. Some people swear that vinyl sounds better than CD's or lossless file formats (flac, ape, etc)
All I can report is that I grew up with vinyl and switched over to CD in the late 80's. My ears loved CD's. I still remember the first 3 CD's I bought, which I had heard on vinyl many times. "Smash Hits" by Jimi Hendrix surprised me when I noticed the backing vocals for the very first time on "Hey Joe"; The Stones' "Beggars' Banquet" made me notice things like the piano during "Jigsaw Puzzle". Jefferson Starship's "Red Octopus", on the other hand disappointed me; the CD seemed to strip some of the lushness of that album away.
In all three cases, it felt like I was hearing the music right for the very first time; vinyl had obscured those sounds in the murk. At the time, people said that CD's sounded "unnatural", but for me, it was quickly the vinyl that sounded unnatural; I preferred digital detail.
That murky quality I refer to is what vinyl fans often call "warmth", and for them vinyl can not be beat.
Frankly, the fact that I no longer have tons (almost literally) of vinyl to store anymore is such a benefit in life. I collect music in .flac lossless format, which is probably overkill. A good mp3 does the trick just fine, most of the time.