Birders: Bird Id needed: coopers or sharp-shinned hawk?

I saw a hawk munching on a robin or maybe starling this AM. the hawk was significantly bigger than it's pray making me think it was a cooper. i think prey was a robin, it was hanging vertically beak-down belly toward me off a branch. hawk has his beak to me. prey didn't look totally black to me, and i think it could have red, but i won't rule out starling. 300 robins everywhere here, few starlings. hawk had a solid grey back. white-looking belly with few streaks. solid yellow throat under the beak fading downward, but grey head. barred black-n-white tail. not sure if curved or pointy tail. i came to the conclusion that the size difference is the biggest clue, and it points to cooper's because sharpies are so TINY. but it still looks like a sharpie to me :( for no reason, or possibly the coloring of the solid grey back and the sharp barring on the tail. so what is it that is at least 2 times as long beak-to-vent than a robin(starling?) beak-to-vent? can it be a sharpshinned after all?