My cats are all indoor, but once in a while in the spring mice movie in and one of my boys has a heyday. Unfortunately he dosen't always kill them and they get loose in the house and I find them dead from fear. Literally frozen in position hiding. Sad. They don't really eat bugs, try to catch them occasionally, but would rather just stare them down.
I do take one of my boys (the hunter) out for walks on a leash, it seems to have calmed him down a bit and he's even lost a pound (he's a chubby). Even so, on his leash he's tried to catch birds, bugs, and the other day we walked next to a pile of branches and he grabbed a big bull snake. He's also chomped on a tree frog, but my landlady helped me get it out of his mouth. He's not hungry, just a hunter. If he were allowed out alone he'd kill all day long.
My landlady has a cat that catches several mice each day, dosen't eat them. The feral mom of my two boys used to catch mice all day, but she'd eat them.