So to answer your question, I've been on some pretty knarly trails with my hawk. Deep ruts, log and steam crossings, steep hills. The hawk handles it with confidence. Now I think the bigger question is how do i tackle these trails, cautiously. I do most of my trail riding at slow speeds so I'm not really hammering the suspension.
I would never dream of riding the hawk like an mx bike. That is left to better bikes,and riders for that matter. I'm in my late 40s so I know my limits, and those limits pair up nicely with the hawk's limits.
The KLX is a superior machine in most all respects. I got my hawk because I haven't ridden in decades and I was not willing to part with $5k to see if was something I would like to or have time to do. Choices are good and it sounds like you have plenty. Hope this helps... Either way, we want photos.