Weasel. Hard to catch (for me) but it will continue killing until it is stopped. Look around for it's nesting area. They usually stay close to their food supply. In the daytime you will probably find it asleep.
There are more expensive motion detectors. I'm assuming they are probably better at detecting movement. You may want to spend the extra money on better detection. I got the cheaper ones and don't regret it. YET!!
When the motion detector sets off the "alarm", you go out and either kill this thing or at least identify it. The other light in the fixture will provide you with enough light to see what you're doing.