Short answer ... unless you absolutely love manual shifting and absolutely hate going offroad, get the automatic on the adventure package.
Long answer ... the 5-speed has several advantages over the auto ... lower 1st gear ratio, cooler transmission temps, 1 mpg more than auto, better road feel, and more control for passing or going uphill. I also think the 5-spd is a better match for the 2006 engine, but that's less true with the new one.
But the auto has lots of advantages too ... easier in traffic, one less thing to worry about when 4-wheeling, no embarrassing gear grind when you miss a shift (not that I ever do that
), no rolling backwards when starting on a hill, and higher tow rating (4500 or 5000 lbs instead of 3000).
As for road feel, the base H3 seemed to soak up the bumps a little better than the adventure package, but not by much.