I keep my cats indoors (we take them in to the garden from time to time under supervision) for a variety of reasons one of them being fluffy cute little murders who kill birds and such just for sport...
There are also birds which are smarter then cats where "killer instincts" don't work on. For example I've seen magpies "play" with cats to lure them away from their young. From the interaction it was clear the magpies were employing strategy while the cat was just reacting.