N8 is right that bird species show different temperaments in the hand, and this holds for raptors as well as the songbirds that he helps to band. Among raptors, larger birds tend to be calmer than smaller birds. This is not always true, as bald eagles and northern goshawks both have reputations for being a bit high strung, but it holds for most raptor species.
Among buteos, red-tailed hawks are fairly docile, which is a good thing since their legs are powerful and their talons are particularly large. They just sit still with their mouths open and their wings spread wide until it is time for release. Red-shouldered and broad-winged hawks will try to bite and are often successful. (Bandages and hand wipes are very useful in a banding station.) The buteo-like golden eagle is also remarkably calm; both golden eagles this week tolerated many curious onlookers and extra measurements without struggling at all.
Accipiters are more likely to struggle and bite, though the majority of both sharp-shinned and Cooper's hawks will tolerate the handling necessary for banding. I have been bitten numerous times (and occasionally footed) by both of the common accipiters. Sharpies often act tough despite their small size, much more so than Cooper's hawks.
Falcons are the most high strung of all the raptors that I have handled this fall. Like N8's chickadees, they are very good at finding sensitive spots when they bite, which they do at every opportunity. They are also very flexible, especially kestrels. Both kestrels and merlins will scold during the banding process; merlins often keep scolding as they are flying away after release. Still true to the size rule, peregrines will not struggle or scream as much as the smaller falcons, but they do hiss (like a cat) and bite. Hissing makes their fish breath even more noticeable. Unlike other hawks, most falcons will perch near the banding station and try to pull their bands off immediately after release.
Those observations, of course, do not hold for all individuals of a species. From time to time we get a feisty red-tailed hawk or a calm merlin.