Rocks and mud or other technical stuff, jeep hands down. But in the open desert I give the H1 the prize. The longer, wider wheel base is better in the sand and you have more room for your crap. Case in point:
My 11000 pound gun truck from Iraq. We ran this thing 90 on the highways and accross the desert at 60 plus.
And as far as the H2 goes, just a Tahoe with sharp corners. H3 just a glorified Traiblazer. POSx2!