"La collina è nostra."
Imagine having bought a Tuscan villa. Standing on the balcony, wine glass in one hand, pointing out to your Italian partner where your wine fields are situated... ;)
I dont think there is much of a difference. I think there is a case where you would use la nostra more than the other, a specific case when you want to emphasize that is it your hill for example is someone asks "who's hill is it?". I don't actually know if I'm correct in italian, but if you know some french you'd understand: "La colline est a nous/ c'est notre colline" vs. "la colline est la notre" Basically there are several ways of saying the same thing.