Why not: "Wolę warzywa do mięsa"?
That's not how we say it, that's a literal translation. We say it as "from meat".
And what with "than"? In this case it's the same meaning that polish "od" or "niż"
Yes, "than meat" = "niż mięso" (with Accusative). And it works of course.
'Nad mięsem' doesn't work?
I'm afraid not.