The 4R is useless offroad, it can barely climb a pebble nevermind cross a stream.
j/k
The H3 has a pretty good advantage offroad if you get the right configuration. WIth 4:1 transfer case and 33" tires. Its engine might be weaker, but it will have bigger tires and gearing especially for rocks. On sand it will not do too well with the extra pork and weak engine. The 220 HP is not what worries me, but rather the 225lb/ft! Time will tell how well it does.
The 4R can cross 16" water with ease, going to 27" is not a problem either. Teh front diff, tranny and transfer case already has breathers up to the high end in the engine bay. The rear diff takes like $10 and 1/2 hour and you relocate the breather to the filler area by the gas cap. The approach angle on the 4Runner is not great at 31 degrees, H3 is 37.5 which is not so super either. The Jeep Rubicon/H2 are probably the only ones with bragging right of more than 40 degree approach angles, the rest of them all are pretty much sucky ( excluding things like the H1 off course). The departure angle on the 4R is misleading as you will tend to drag your spare and tow hitch a bit, so no real biggie to be honest.
Also on the 16" wall climbing nonsense, I have yet to see nice 90degree steps on a trail. Most of the time you will aproach it when the vehicle is already at an angle of 15 degrees or more making the 16" step a lot smaller.
I can't wait to see the H2 guys now complaining about the H3s making the Hummer name sound sissy. Now they know what the H1 guys felt like.
Besides if you want to do wheeling, you might want to check out the new FJ Cruiser. It looks like it will have a lot of potential, still waiting for final specs. But angles, clearance will be improves, less weight, shorter wheelbase ( not always a good thing), diff lock, 32' rites and ATRAC by the looks of it. Probably std sliders on certain models too.