I've had no issues with ATs on the trails I've been on or in mud, and they're better in the snow/rain than MTs. I don't really miss any of my old MTs, but I also don't really like mud so tend to avoid that.
On harder rockier trails the larger tread blocks of most MT's tend to smear and grip a bit better than the smaller voided or siped tread blocks of most AT tires..
I put 33 ATs on Katrina, but when I complete the Blue submarine she'll be wearing something meaner .... but as you say, will it actually get you further? No, traction is rarely the issue; articulation and hang-ups are.
The guys above pretty much covered it I think.
Today's extra aggressive ATs like the ST/Maxx and Duratrac perform nearly as well as a true MT off road and better to much better in rain/snow either on or off road. They are also generally quieter and have better road manners as well as having longer tread life. I'd also expect a bit better gas mileage with an AT vs MT.
In true mud they won't keep up simply due to the lack of clearing voids. And in really rocky situations a MT's softer compound can provide more grip in addition to having larger biting edges to claw with. They also tend to have more aggressive shoulder blocks which can help in some situations.
And a MT should have a little heavier construction, particularly in the sidewalls, which is always good in gnarly terrain.
In short, an AT is probably better for 90% of the average truck's use but if you want the best in the toughest conditions an MT is still the way to go. Were I building something like you, I'd be looking at an MT. But on my LR3 I'll most likely stick to on of the more aggressive ATs.