I don't have any Hawker models and haven't played them (so I won't comment on tactics), but from what I know about playing terrans and looking at the alliance pdf.
In common:
Both fleets are generally slow, have turrets, have weapon shielding available to them, have nukes, and have generic primaries as a general rule. Note, Hawker are natural allies to Terrans, so they can be mixed and matched 50 / 50 in a Terran fleet.
Differences
Hawker is part of the alliance fleet, meaning after you meet core requirements, you can mix and match other alliance squads as you like
Terrans rely more on shields - Hawker trades some shields for a higher CR rating
Hawker has Cyber Weapons
Hawker tends to have upgrades for more HP and MV, while Terrans have more upgrades for shields and beams. This gives Terrans a bit of a range advantage with upgrades, while hawker ends up a little more durable and can make up some of the speed / range deficit by pulling ships from another race
Hawker ships tend to be expensive, especially with upgrades, including the frigates which can hurt when it comes to activation count. Terrans can fill minimum requirements more cheaply.