As my teacher put it, "Modern instruments may have a voice that's as good as an antique's, but they only have the one voice. Due to how age works with violins, antique violins have many beautiful voices. In a couple hundred years a 21st century instrument with the same craftsmanship and material quality as Strads and del Gesus—and these instruments do exist—will be as good as a the Strads and del Gesus do now. But right now that's not the case."
And I've found this to be true myself. When I pick up a modern violin it might take some time to figure out how to make it sound best, but then I'm done. With an antique instrument, it turns into this indefinitely-long relationship where I continuously learn new things and find new voices and tone colors in the instrument. When I returned the aforementioned Gagliano after three months of heavy use, I felt like I'd only just begun to discover the range it had available.
And it really is about age for age's sake, not quality. I own a good-but-not-great Edinburgh-made violin from 1807 appraised at $15K, and I've seriously played a modern-made violin appraised for $60K. The "default voice" of the $60K violin is better, but the antique instrument is definitely the more versatile one.
I know we like to be objective and scientific here on HN, but don't discard the fuzzy talk of "forming a relationship with the violin" too soon. Even if we don't understand the science behind it yet, it seems that there's something to it.
A better experiment that'll never happen because of logistics:
Present a professional violinist with ten antique violins, ten modern violins, and a range of high-quality bows (the bow plays a HUGE role in how the violin sounds and responds). Give him/her a few hours to choose the favorite of each type of violin and a complementing bow. Let him/her play both violins for a year and then report back on which was preferred. Repeat for a statistically-significant number of violinists.