The type of birds that prey on pigeons and will eat pigeons are the birds peregrine falcons and red-tailed hawks.
The peregrine falcons and red-tailed hawks diet mostly consists of pigeons and pigeons are the most common bird they will eat.
However both the peregrine falcons and red-tailed hawks will eat other birds such as starlings, blackbirds, flickers, and blue jays.
So they will consume and prey on any type of bird that they can get but pigeons is mostly what the peregrine falcons and red tailed hawks eat is the pigeon which is what they prefer if they can get one or two or more.