I think either bike would be fine, I would look at the components that are on the bikes.
My wife was looking for a full suspension and she was considering a Kona Dawg, it seemed like a nice bike. She ended up getting a Santa Cruz Superlight Juliana. Either way get the bike that fits you the best and has the best components.
If you want any prices on Trek let me know. I can get them out of a shop by me and will beat anyone's price. I can get also Gary Fisher do not know how far you are from Joliet Il or can work on shipping I do know a lot about bikes in my opinion for the 1000 I do not think I would do a full suspension. I would do a better hard tail. I do have a lot of experience in the bicycle industry if you have questions. Giant is the manufacturer for most bike shop quality bikes.
These are very different kinds of bikes, one is a 4" travel cross country bike (the giant) and the Kona is a 6" travel trail bike. I'd pick which one is better suited for your riding. I do the trails in Marquette and Copper Harbor on my cross country bikes, I don't feel the midwest needs much, if any, more than that.