Aloha Airlines is one of the state's two primary interisland carriers, the other being Hawaiian Airlines. The two are actually pretty similar: both fly interisland and to the west coast; both have all-jet fleets; and both have struggled financially (Aloha is undergoing restructuring while Hawaiian is just emerging from restructuring).
Aloha used to have the better reputation of innovation (drive-through check-in, for example) and efficiency, but recent turmoil in the industry has eroded those advantages.
Now, the decision on which carrier to use seems to come down to when you need to fly -- both airlines reduced their schedules to eliminate the overlap in their schedules.
TIP: You can redeem United miles for a round-trip ticket on Aloha. At this time, it's 5,000 United miles for a round-trip, but that's subject to change, of course.