1) They give a flyer lots of room to maneuver.
2) Likewise, there aren't a lot of places for prey to hide.
Personally, I find the idea of giant hawks dive bombing some merchant ship or fishing vessel that strays too close to a seaside eyrie fraught with potential. Let's look at the stat block, shall we? (LL81)
No. Enc.: 0 (1d3)
Movement, flying: 450' (150')
Armor Class: 6
Hit Dice: 3+3
Well, right off the bat, did you SEE that movement rate?? One hundred fifty feet per round! And you thought centaurs were fast! Basically, a character is going to get one shot at these suckers before the range penalties kick in (if the birds aren't out of missile or spell range entirely).
A normal encounter is 1d3 giant hawks together. Probably all riding the same thermals. They might not work together, but birds are greedy, and if one goes after a potential meal, the others will try for it too (or try to take it away from the first bird). Their morale is low enough that they might get scared away, but they might carry something (or someone) off with them. While they cannot carry off a full-sized man, gnomes and hobbits should beware.
The birds' HD and AC aren't superb, and neither are their attacks/damage, but in the aforementioned sea encounter, their mobility is that much more useful when characters are confined to a ship. If a character is struck by one of these raptors as it dives, and he is up in the rigging or near the side of the ship when it hits, any GM worth his d12 should force a saving throw or ability check to avoid being knocked off. (Sure hope he wasn't wearing plate when he fell in!) If the character is hobbit or gnome sized, a hit should allow for the bird to fly off with him. Personally, if the bird still had movement left that round I'd let him get airborne with his prize (but I'm kind of an SOB). The victim, if still alive, can certainly try to fight the bird off while in its clutches, and the hawk might make a morale check or saving throw to hold onto something that's really hurting it. However, consider that if the hawk has more than a round to get altitude, do you want it to drop you?
I mentioned being stuck on the boat while this is happening. Wizards should note that flinging are of effect spells like Fireball at these creature might cause some nasty collateral damage. (Burning pitch-soaked timbers, anyone?) A circumstantial cover bonus to the flyers is also probably in order for any masts, sails, and rigging between them and any archers on deck.
For the desert encounter, look to your camels. Even if the hawk can't carry it off, most raptors would be fine with killing the beast and then tearing off a hunk of meat to take with. If a pack animal is laden with provisions, a saving throw might be in order to see if those nasty talons have torn up your waterskins. (see "SOB", above)
Lastly, I should mention that these are not supernatural creatures, but big animals. They don't attack out of malice, but hunger or self-preservation. Conversely, a mage with Charm Monster or a druid with Animal Companion/Friendship could play merry hob with a few of these following his orders.