Stradivarius instruments deserve being put on a pedestal for historical reasons. Stradivari basically defined the sound of the modern violin, using flatter arching and f holes with smaller hole areas than the Amatis, which resulted in a significantly more powerful instrument that was better suited to playing in a concert hall (vs. the chamber music of earlier times). Stradivarius violins are also noted for their extremely fine craftsmanship and attention to detail. The majority of modern violins are still modeled after Stradivarius examples (with a probably smaller number modeled after del Gesu instruments and some other makers). Most top soloists play on (heavily modified) Strads, and so it seems pretty clear that, at the very least, Strads are not holding any soloists back - and that is not the case for Amati instruments, for example, which despite being coveted for their age and history just don't have the same power and sound projection as Strads.

But, as other comments have said, there have been at this point a good slew of blind tests, and Strads are hardly ever recognized better than chance when compared to modern instruments, even when played by experts and judged by experts. People have been studying and modeling after Strads for so long it would be pretty shocking if we couldn't make instruments that sounded as good. In my mind that doesn't make Strads any less valuable - an original Picasso is still valued so highly because it was created by the master that invented Cubism, but that doesn't mean that a modern painter couldn't create a Cubist painting that was "just as good", objectively.

Only a handful of controlled tests have been conducted and listeners failed to identify or prefer the Strads. None of the experiments were very big so there might be a perceptible difference that can be detected with more statistical power. Blinding the eyes and noses of top level musicians might bias the results.

It is very difficult to obtain access to the instruments. The general sentiment from musicians and collectors seems to be that they don't want a bunch of scientists to come into their world and tell them that what they are or are not hearing or they just don't understand why controlled tests are required.

A bit of engineering and a lot of myth and degradation due to time.

The engineering seems to be a combination of genuine construction advances and the usage of wood that was abnormally dense due to having been grown during a big drought.

This, of course, contributed to the "myths" around the Strads with the varnishes, techniques, etc. supposedly being "The Thing(tm)" that made Strads so much better.

Finally, wood degrades with time--period. It doesn't matter how much you try to preserve it, it's just fact. The current Strads are either "Ship of Theseus" type violins, or they are heavily degraded.

At this point, modern luthiers create better instruments than even a Strad in its prime. They have access to better woods, better glues and finishes, better tools and training, better analyzers and better players than anyone in the time of Stradivarius.

When played as close to double blind as is possible, the data comes back with modern players preferring modern violins made by modern luthiers over the old Strads.