I’ve been lurking away at this thread, because I’ve played violin, and can still make one sound not quite like a bag of cats. So, while I don’t know what I’m talking about in any depth, I’m in its neighborhood.
Strads and their cousins were the standard as tools around 1900, because their reputation was solidly established. Due to this reputation, most violin makers began to make their violins as some sort of a Stradivarius copy. I played a Roth for a few years. Roth pretty much only makes copies of two different Strads at different price levels. Some of them were amazing, some were merely OK violins, and the price level doesn’t really tell you much about which was which. They’re hand made violins, out of variable materials. The more experienced luthiers build the more expensive violins, but they built violins after lunch on Friday, and the inexperienced guys sometimes hit it right. My Roth was a cheaper 70’s model, I bought and sold it for $350 during the 80’s, but it is that magical one that I let get away. I’ve played some budget and nicer violins since then, but that one sang. I think I probably placed at least 2 or 3 seats higher in orchestra because that instrument worked so well (yep, response even works when you suck).
The point to that is, the sound of a Stradivarius is kind of built in to what we expect a violin to sound like, but he himself was only partly sure what made that sound. Not all of his instruments are equal, and we’ve been trying to figure out what makes the special ones special for more than 100 years. Companies like Roth could get very close, and possibly surpass the original sometimes, through emulation and experimentation before the 1970’s (indeed, the most valued ones are pre-WWII). The examination of the original instruments has continued in earnest since the 1970’s, and our understanding of the materials involved has increased by leaps and bounds. If we couldn’t at least come close to a Strad* with current knowledge, processes, volume of attempts and the amount of effort devoted to examining them, we’d be pretty poor monkeys.
So, I do think that a lot of what makes a Stradivarius so good is partly because they are so damn old. Any stringed instrument that doesn’t have self-destroying string tension that has been maintained and loved for that long is going to have some special qualities, even if it’s not one of the greats of the marque. Do I think you should go out of your way to play or listen to the actual thing at this point? Nah, you should base it on the performer, if you’re just listening. If you’re playing, and footing the bill for the instrument (it seems that most people who play a Strad in a performance don’t actually own them), I’d say limit yourself to the best violin you can find for less than $1500. In the end, like the mighty Chet and Jascha explained, it’s the person playing the instrument that makes it good. Until then, it’s a pretty box. If Yehudi Menuhin was (alive and) bowing a banjo, I’d find a reason to show up.
*Or the moving target that is a PAF (or any 50’s pickup, it’s not like quality control was their watchword ;))