I remember watching an Igor Oistrakh masterclass where he complained about the sound a young violinist was making on her cheapish violin. He said "play it like this" and then played the same note on his vastly more expensive instrument. I think everybody in the room was thinking something along the lines of 'I'd like to see him make that sound with the instrument she's playing."
The biggest physical thing to stand out when learning is that you make slightly more tinny sounds on smaller violins, and you don't typically hit a full size violin until you hit puberty.
If I were to guess, his violin does sound better, but the skill would make the biggest difference in the two situations.
Yo! Oistrakh. One of my favourite violinists. I have noticed the following with my 10 year old's violin teacher (who is a really good violinist). To show him a certain technique during her lesson she reaches for her instrument instead of his. Especially for a bit challenging violin part, I guess she can confidently show a technique better on her own familiar instrument.