Albeit slightly boring, the Stars have a much sleaker look than the Blackhawks. I've always found the Indian head a little clunky and intricate, not to mention its lack of a defined color scheme.
Chief Black Hawk may have been a tough son of a bitch, but a Star is a giant all-consuming ball of fire.
The Blackhawks get their name from Chief Black Hawk who was a Sauk warlord in the area of what is now Rock Island, Illinois which is less than 200 miles from Chicago. Not bad. On the other hand, the Stars take their name from predecessor Minnesota North Stars. I think it works great, what with Texas being the Lone Star state. The only drawback is that the team name is spelled out in the logo and, by and large, I'm not a fan of that. Still, they squeak by with the point.