I was thinking that somebody with the tools should purposely record a song into two different formats at the same time. You probably know where I'm going with this...
Why not do a recording that goes into an analog console and tape machine, and a Pro Tools system. Set it up to be as simple as possible to rule out performance variables, etc. Probably take an old 60's pop song that's real simple and let a band take a stab at it while you feed into an analog and a digital system.
You could even take it a step further and continue the process through the mastering and delivery medium.
I think that even on a multitrack situation where there are two many variables, the results would still produce subjective differences we could argue over.
But a live to two track situation would probably be best.
It's gonna take a hell of a studio to get it done. You'll need a complete modern digital system, which is easy enough. But a complete analog signal path isn't as common. I'm talking analog console, tape machine, plate reverbs, analog/tube effects, etc.
Master the digital version and send it to CD/wav.
Master the analog version on send it to LP.
Playback and see which sounds better.
I think a good analogy for all this is you can get a fancy digital watch that has a gazillion features like gps, phone, HD video, or you can get a swiss watch that was designed by craftsmen to do one thing and do it right.
I still contend that the analog/lp version will sound better. Not a bit, but a very noticable difference. If you don't think so, go look up a song on YouTube and play it. Then do the same search with the world vinyl. The vinyl always sounds better. Wider, depper, more rich. It's not just the eq, there's a lot more depth.