Although I will say that the loudness factor will always be decisive with the listeners.
Loud music always sounds better. This is because at a louder volume, the human ear will pick up the widest range of frequency. Humans are most sensitive to the 2-5 kHz, so frequency from that range played at the same decibels/volume would sound louder to humans then frequency of the same decibels/volume played at different frequency. however note on the graph below as the decibel increases on the graph, the flatter the equal-loudness curve is. This is because at louder volume we perceives frequency outside the 2-5kHz range at almost the same detail as the sensitive frequency. this is how the loudness wars started in production by exploiting this curve and people will often feel that louder mix has more "detail" as they can hear the entire frequency spectrum more clearer. That's why the saying in audio production - you can't compare two mixes unless you play them on the same volume. If a mix sounds louder, it would sound better, however if you play the same mix at the same volume (by turning the volume knob up for the softer mix), often the mix with more dynamics sounds better.
The same principle will apply to the Stradivarius vs modern instruments. for a fair test, both would be recorded and then played back to the audience at equal volume. Then the audience can choose which timbre they prefer.