I have 200 vultures, both black and red headed one's, that roost beside my house at night. They have never bothered my chickens, and the black one's are smaller than red one's from what I can tell. However, while I would blame a hawk before the vulture for your losses, I wouldn't rule it out. I have seen and heard of freak vulture attacks. Though very rare.
You cannot shoot a vulture legally, but you can scare them away with loud noises such as fireworks. It won't work the first night you do it, you have to be patient.
I keep a loaded .410 shotgun handy for just such instances. Whether it's vultures during the day or coyotes at night, a round fired off in their general direction works wonders to keep them at bay for weeks. I imagine firecrackers would work well too. I've never had vultures go after my chickens, but I prefer to not wait until I see it, so I send out the "not welcome" mat whenever they start hanging around. Of course, in a more urban setting a shotgun may not be a viable option, but I'd try firecrackers for the noise they make.
I've seen caracaras around sometimes. They're only found in the very southern states as far as I know, so if you're in the U.S and not in Texas, Arizona or Florida, I doubt it's a caracara you're seeing. I don't believe they're in Europe, either.