Most of that analogue 'magic' comes from the original circuitry. The subtle little nuances of tubes and transistors, minute alterations from imperfect voltage signals, and the general difference of a coloured analogue signal path over pristine digital, is what creates that fabled warmth.
There are strong arguments from those who work with analogue that digital computation will never quite replace those tiny details that make analogue signals, and to a point, they're probably right. Computers, however, have come ahead in leaps and bounds in just two decades, and we will eventually reach a day where digital processing and computation renders the old format completely redundant.
That there, though, is another strong aspect of analogue sound: the rose-tint. It's no secret that if somebody grew up surrounded by the hum of hardware studios and tape reels, they're not going to catch on to digital sound as fondly as others. There are numerous blind tests out there to show that, even if only the slightest bit off their hardware counterparts, software IS almost a perfect replica, and near-indistinguishable in difference. Yet, there will always be those few who rocked the Oberheim or Prophets in the 80's that swear by the original thing, even if it's getting matched.
I think it comes down to individual perspective. I personally think we are a little way off perfecting analogue signal in the digital realm, but the freedom digital offers trumps most to all of what analogue gear offers. I too have listened to 'the good old mixes' from the likes of Abbey Road and Ocean Way, and can't help but think the appeal simply comes down to nostalgia. There is a certain element of warmth and body to them, but nothing that would have me wanting a real console and cutting tracks to vinyl. I think I'm just a sucker for pristine, intricate sound though!
