If you have mixed or "single stream" recycling the cases will end up in the metals area and get properly recycled. They might end up mixed with steel and alu, but from a recycling standpoint that's minor. If you are single stream, you just need to pay attention to what you local facility cannot handle. Plastic bags are usually a super no-no (gums up the rollers) and lots of places would like you or demand that your glass goes into dedicated glass containers.
Here in KC we have several community recycling drop off centers that allow you to dump mixed metals into a big container that the metals recyclers pay good money for. So I have a couple 5 gal buckets that are my "metals" buckets. Wire, nails, screws, brass, bullets etc etc go in there. Brake rotors, anything cast iron, you name it, they'll happily take it. I just fill my buckets over time and give it away now and then.
I don't think its worth the trouble to lug old brass to the metals recyclers -- just not enough weight to justify the trip, but I am nearly certain they would buy it as recyclable brass. Brass is quite valuable for recycling, but our rifle brass doesn't weight much compared to industrial fixtures, plumbing etc etc.......