I don't have a lot of experience of old Fender basses - I'm primarily a guitarist. Old Fender guitars of the 6 string variety tend to be a lot more expensive than the basses. I wouldn't personally spend that much, but I do have to say that a 50's Tele I once tried was probably the best sounding electric guitar I've played. There does seem to be something special about the best of the old ones.
The whole topic of old wood is discussed to death on guitar forums. There are those who say that the wood is better. Whether that is because of quality in the first place, and all the good stuff has now been chopped down, or whether it is down to the way it ages is another matter for debate. Whatever the reason, in the 6 string guitar market, those old ones fetch a fortune - but a lot of that is because they have now become collectable. That seems to be feeding over into the bass market as well. There is an element of "what the heroes played" in it as well. Some guitarists want 58-60 sunburst Les Pauls because that is what Clapton played on the Beano album. Some bassists want vintage P basses because that is what Jamerson played.
I can only ever recall having a go on one pre-CBS Fender bass. What did stand out was how light it was. It really was a featherweight. I don't know whether that was how it had always been, or whether it had lost moisture content over the years. Lighter weight instruments like that might well have a different tone. Is it better? That's probably subjective.