Anywhere from 35% to 60% reduction in weight, depending on the design. Some designs are partial brass, like shotgun shells, for more dependable extraction. Some have brass necks, to better handle heat at the barrel throat. Cost is a factor also. Another is consistency. Polymer can be made to closer tolerances and it doesn't lengthen under pressure, so tighter headspace tolerances can be used, which I've read (I am not an expert in this) can theoretically improve accuracy. Also, polymer does not transfer heat to the chamber like brass does, so theoretically, chambers will last longer.Bummer about the end of the Lake City surplus brass. That's how I built my stockpile.
Is there any advantage to polymer cases other than weight and I suppose cost?
I don't know how much of that is true and how much is contractor marketing hype, but that's what "they" say. The weight reduction seems to be the big thing and the most solid claim.