There's no question between the two. Personal opinion,, I don't think the trail hawk is a very efficient tool at all. Kinda fun for throwing, but it's too light and the bit isn't wide enough to be a real effective feller. If you like hawks though, check out the HB Forge Shawnee.
If you do decide on a dedicated axe, there are a few brands worth checking out.
Barco/Kelly, Husqvarna, Hultafors, SA Wetterlings, Sandvik/Bahco, and Council Tool all make very reputable retailed axes at a price point significantly lower than GB. You can buy a USA made Kelly Woodslasher boy's axe, a Bahco or a Council Tool Hudson Bay all in the 40 dollar price range. If you want to get more in depth, hit the Axe and Tomahawk subforum-tons of incredible information on there.