Believe it or not, there aren't too many resources stressing the differences between vintage and modern saxophone mouthpieces. What makes an old Otto Link from the 1950s justify a $500-1000 price tag? Why are the new ones only $200-250?
Is there a tonal advantage to playing through a really old one? I would think the opposite, as modern technology would make modern mouthpieces more consistent.
Honestly, it's the combination of being a collector's item, and they were made very well, and it's quite likely that it's been refaced by a master refacer at that price which is worth a lot too. If you don't care about the collector's item part, you can get just as good a mouthpiece from a modern link copy, but if you want it just as good, expect to pay what is still serious dough ($400-1000 probably). Modern copies that I would put in the same category of quality include Theo Wanne, Aaron Drake, Navarre, Ted Klum, and Mouthpiece Cafe, among others. Very small physical differences make a big playing difference in mouthpieces, to the point that the skill of the finisher is significant. When you find the right high end mouthpiece for your horn and embouchure, you won't believe how well it plays and $500-1000 is totally worth it.
This is a difficult question to answer in a non-subjective way. What I will say is that there is a bit of a legend among saxophone players that old saxophone mouthpieces were made with materials (perhaps toxic materials...) that are not able to be manufactured today, and that these materials simply sound better. Some of the mouthpieces are physically rare as well.
