Well, the Stradivarius thing is complicated. Unquestionably, the age of the instruments is a big part of their sound. He was an exceptionally gifted violin maker too, and that is a big part of it. But every single Stradivarius violin in existence has had its neck replaced. Or at least every one that is in use in a professional orchestra. (Back in the late 1800's, Paganini popularized a longer violin neck, which has become the absolute standard since then.) They are also all hundreds of years old, so they have all had major repair work done to them - and the violin world doesn't have the same level of the "cult of originality" that the vintage guitar world has.
And then, of course, is the expectations that people bring to a Strad. Are his violins REALLY that much better than any other builder of that time? Probably not enough that they should cost double or triple what another excellent contemporary violin costs. But, just as the Gibson, Fender and Martin names command a premium for guitars, Stradivarius demands a premium for violins. I mean, what other Violin makers names can you think of? The only one I can think of is Bussotti, and that's fictional! (The Red Violin - great movie!) Now, part of that cost difference is because a Stradivarius (or a Gibson, Fender, or Martin) is a much better investment for a collector, because it will hold its value better - which has nothing to do with how it sounds (I've played some 1930's Martin's that were dogs - woof!) - but the perception that they are somehow sound better is out there, and is pretty tough to get rid of, and not without reason; they are all excellent examples of their type. So I think a part of those brands popularity is to do with people either not trusting - or not using - their ears, so they want to rely on other people's perceptions, or to rely on the fact that they've always been told "Stradivarius is better!"
But age does make a difference, and it continues making a difference for as long as the oldest instruments I've ever tried. They keep drying out, they keep moving, and they keep sounding better and better. Drier is the only word that I can come up with for it, but its a great thing!
Gabriel