Another indicator is falcons have a protrusion centered in each nostril which doesn't appear to be present in the photos.
The beak would also be an indicator but I can't see the necessary detail with this screen. Falcon beaks look very much like conure or cockatiel beaks with a zigzag jag in them that is lacking in hawks, which have a simpler hook.
The photos don't show much about the wing shape so I can't tell anything by that.
Birds in general appear to have the ability to see into the infrared parts of the spectrum, not just predatory species. Bees see infrared too, and to them flowers look much different, and come complete with bee-readable directions for entry. For some reason God decided not to give such vision it to us, unfortunately. I suspect in birds it may also serve as a means of sexual identity in species which to us appear to look the same in color and markings and song. The birds can certainly tell the difference without resorting to blood tests. If we could see infrared maybe we could, too.
The bird in your photo has eyes that are small in proportion to its head, like many hawks, though Sharpies are unusual in having rather large eyes for their head. Falcon eyes are very large in proportion to the head, which this bird's isn't. Falcon eyes bulge out farther than does this bird's, as well, so from the front this bird's face doesn't resemble a falcon. Even sharpie eyes bulge more than this guy's. Young sharpies tend to have pinkish or olive ceres, rather than yellow as in your photo [or what I think is yellow with my monitor, which wants to make everything kind of pink!]. But the eyes in the photo do look like those of an immature Cooper's hawk in size, shape and color. Immature Cooper's have yellow ceres, and I think immature prairie falcons have gray or bluish ceres though adults have yellow.
The bird in your photo has sparse white spots on its back, a sign of immaturity found in Cooper's hawks and I think the smaller Sharpies' too. I don't recall this being a feature in falcons of any age. While the bird in the photo has teardrop markings on its breast and belly that do strongly resemble those of an immature prairie falcon or even a merlin, so do immature Cooper's and some other hawks. Unfortunately many guidebooks don't have good photos of immature birds, so it pays to be cautious about using belly markings as the sole identifier. Note that an immature prairie falcon has blueish feet, not yellow. A mature prairie falcon's belly and chest markings look more like small chocolate chips than the teardrop shapes in your photo. Likewise a mature Cooper' hawk has totally different markings when they mature - their dark teardrop markings become brighter, finer rusty horizontal barring as they age and older birds also develop a dark cap on their head which is absent in the young. An immature Coopers or sharpie, for that matter, has yellow feet and the same teardrop markings as in your photo.
The prairie falcon has finer horizontal barring on top of the tail than this bird appears to have, IIRC. The barring in the photo is much broader and the bands fewer in number-looking more like that of a Cooper's. Most falcons prefer open country and rely on speed and altitude to overtake prey in a dive rather than ambush, but is true the prairie falcon is an exception which can navigate more crowded country than its brethren and it does ambush like a hawk. But then, this is perfect habitat for the abundant Coopers' too. Unfortunately the description of the habits of the bird in your photos doesn't help as the low-level flight behavior- 2 ft off the ground- is also similar to Cooper's, and hunting from ambush is also a shared trait. Both are extremely agile and swift though the falcon can dive from great heights and achieve impressive speed, something it doesn't much need in your yard or heavy cover. The Cooper's is notorious for hanging around birdfeeders and aviaries particularly when young and not so skilled, and for speedily capturing doves and the like. It just seems that most factors most notably the eyes point towards a hawk like an immature [not adult] Cooper's.
I reserve the right to be horribly wrong but that's my logic, anyway.
Thanks, best analysis I’ve seen so far.
Periodically we’ll get a red tailed hawk, but there must be a group of nests with this type of hawk/falcon in this area.
They seem to have a route about a mile in circuit, where they will fly several hundred yards to a birdfeeder, then hang on the eave or in a limb, or sometimes even on the ground, or a rock outcropping, scanning for prey, as long as perhaps 90min, but generally about 12 minutes, then off to the next hunting spot.
These definitely have yellow on talons, beak, and iris.