Luckily, your rich uncle Hellbie has given all of them extensive field testing because DUH. ;)
Eyrie: Very odd design, too small for the kind of brawling that its layout suggests it's good at. Talons allow it to take a leg off another light in a scrap though, the lasers offer hefty punch, and the ATMs allow for either a close-range wallop or a long-range peppering as you advance, depending on your battlefield and preferences. Not a particularly good scout design, but decent as a scout hunter.
Gyrfalcon: As I said, one of the most blissful designs in the game- as I cover in my article, if you liked the RFL-3N Rifleman you'll adore this. Over/under large laser/autocannon in each arm, how familiar! Except both weapons reach well past 20 hexes, so you can alpha a target at ranges where he can't reply with anything at all. And thanks to the mobility, jump jets, MASC, and heat sinks, you can keep that up as a sustained barrage and keep pulling away from the enemy to HOLD that insane range. Blissfully good design in the hands of a good gunner and smart tactician.
Jade Hawk: Varies by version, obviously, but generally a close-range nightmare that would finally give a Berserker pilot something to blanch at. Massed SRMs and lasers with good mobility and tough armor? Yes please. Advance under cover from Gyrfalcons and go absolutely bonkers until your target dies or you do. It's very Hunchback IIC-feeling in a way- it's got severe limitations and yet in its narrow role it's utterly horrifying.
Shrike: Did you like the Executioner's approach towards assault-weight units, mobility over raw power? You'll love this then. Did you miss the stalwart-advances of Warhawks and Dire Wolves? Pass on this. Firepower isn't particularly overwhelming (though similar to the Gyrfalcon), but it can find places to fire what it has that most assaults simply can't. It's an oversized heavy- using it to go toe-to-toe with something similar sized will end badly, so you've got to be smart about using it. A well-used Shrike can be dominant, a poorly used one is just a waste of BV.