Until about 30 seconds ago when I received the New 52 Hawkman, I thought that it was only Hawkgirl.
Why wasn't Hawkman featured in the cartoon? What made DC use Hawkgirl instead of the other Hawk-characters?
They wanted to get away from Aquaman and use Hawkman, but were not satified with a lineup that only included one woman (Wonder Woman), so decided to use Hawkgirl based off the Silver Age version known as Shayera Hol.
From the Wikipedia article:
This new animated TV series brought all sorts of new characters. Ignoring the sidekicks, pets, and other elements of the earlier Super Friends show, the line-up of this new JLA adaptation was created with two things in mind: to pay tribute to the original line-up of the Justice League of America while also reflecting racial and cultural diversity. Significantly, the well-known superhero Aquaman was left out of the lineup (although he would become a member of the team on Justice League Unlimited), and was replaced by Hawkgirl, the team's second female (along with Wonder Woman).
And from the Hawkgirl article:
Her personality was completely redesigned for the series by the producers, who wanted a second woman for the team (taking Aquaman's place) to contrast with Wonder Woman. While Black Canary is traditionally more associated with the Justice League, the producers preferred to have the Hawk family represented.