Really depends on the individual birds in question IMO. A red tailed hawk for example is really best optimized for prey on the ground like rabbits. On the other hand, a peregrine falcon is optimized for aerial prey and they eat everything from hummingbirds to geese

Mostly less efficient vultures, but way more magnificent, so they've got that going for them. (In Australia, so the Wedge Tail eagle is the niche filler and very much a scavenger, always a pleasure to see tho)

3 crows that hang out near my house and join my chickens and ducks when I toss scratch and treats out have made it their mission to keep said birds safe.

Wife and I watched them hassle a hawk until it flew away, gen they came back and chilled on our fence. Tossed them some French fries for the work well done

I'm not super familiar with falcon, it was mostly red tails and sharp shinned hawks where I grew up. Smaller birds were always hyper aggressive with the larger predatory birds. I assumed they were trying to chase the larger birds away from their nest or out of their territory. I've never seen a red-tail go after a bird. Its usually snakes, mice, and rabbits.

Robins are aggressively territorial. Pretty much every time you hear them chirping it's either saying "FUCK OFF!!!" or "FUCK ME!!!".