Of course you can, they sound different. Put two 63 jazz basses next to each other and they will sound different to each other. Get another newer jazz bass with a pickup made to sound vintage and it will sound different.
The difference is whether there is something totally unique to them then you can play 10 basses blindfold and say say 'yes those 5 are vintage, and these 5 arent'. But you can't, I am sure that noone can.
Because they love that bass and they can afford it, they are players not collectors, but I think that will tail off with the current prices, the players will start selling off their old basses and just taking cheaper, less nickable instruments on the road, because that makes sense. Many people stopped taking expensive instruments out, as mentioned, david gilmour sold his rare strats for charity and plays new ones, he still sounds exactly the same.
Even if you 100% believed that a vintage fender came up with a totally unique sound that nothing else could make, you can't possibly beleive you could hear that when it was gigging when half the time you can't tell if it is a bass or not!