In its class there is nothing better with the exception being the four door Wrangler.
That's more of an expression of how anything with 4 inches of clearance is being called an SUV. Underneath an H2 is just a Tahoe chassis and it doesn't have the suspension travel to be any good. Sure it has 4WD and a low range gear box, but while that's a requirement for a good fourwheeler, it does not necessarily make it so. The basic Wrangler Unlimited is fairly competent, but it is hindered by small tires and no locking or limited slip diff. Upgrade to the Wrangler Unlimited Rubicon and you have a serious trail machine on your hands - serious armoring under the vehicle, heavy duty suspension, wheels, tires, and axles. You get locking diffs, low range gear box, a thicker radiator (3 core), oil cooler, and other goodies.
The H2 was never designed to go offroad. If you look at it all they have done is make a body that looks higher off the road than it really is. The vehicle looks disproportionate in every respect and they are notorious for cracking the steering knuckle on something as minor as a
drive thru curb! (It happened just 15 minutes from my house). I've seen them pop tie-rods faster than a Hollywood trophy wife does valium - and on stuff that would not even phase our 14 year old stock Land Cruiser. Trust me, the H2s are a joke in Moab - you never see them down there unless they are towing a dedicated trail buggy. I have
never seen an H3 down there. From what I have seen of the Hummer line (with exception of the H1, which is more military than civilian) the platform does not have the flexibility in the suspension to be very capable offroad, their ground clearance is pathetic relative to their height, the interior volume is surprisingly cramped relative to their size and the visibility is about the same as being inside a concrete pill box at night with your helmet over your face.
They were designed to be looked at and that's it. The styling makes it difficult if not impossible to see obstacles anywhere close to the vehicle making critical wheel placement all but impossible without a spotter (assuming you can see the spotter).
I would put an H2 head to head with our Land Cruiser any day of the week - and Hummer has had 14 years more development than our Cruiser.
Fun Factoid: I have seen more Suzukis off road in Moab than I have H2s and H3s combined.