This is how it would look Saturn if it was at the same distance as the moon.
We'd probably on the same plane as the rings, not on an eccentricity, so won't see the rings.
I have a feeling Earth's gravity would also disrupt the rings and cause them to disintegrate pretty quickly. Also, Saturn's gravity would cause insane tectonic and volcanic activity on Earth, basically turning it into Io. So yeah, there's a number of reasons we wouldn't see the rings.
We'd also be rotating around Saturn (not the other way around) and be tidally locked with it, so... say goobye to tides, sunrises, sunsets, etc... well, at least for a few years, then we'll have dark for another year or two.