One option was RV which is quite close to upgrading horses. I said similar ability not the same. it's hard to measure abiltity in percentages. Quoting manufacturer's manual:
While under axle clearance is somewhat(1/2") better on H3T. PW has it beat on running clearance by good margin. Although that figure just feel a bit too low. Prob measure so something like low hanging leaf mount.
Still although RTI is not specified for H3T (stock H3 is about 450) I'm sure it's quite a bit less for H3T then PW.
As always specs galore but according to
http://www.fourwheeler.com/roadtests/129_0903_2009_4x4_pickup_truck_of_the_year/viewall.html RTI is 417 and breakover is only 20 degrees. Which does indicate noticeably smaller running clearance.
Honestly 2.72 v 4.00 would only matter in really serious rock crawl situation. Do you have to do that regularly? IMHO having only really low option sometime can be detrimental as well. I previously owned Montero 1.9, Land Cruiser 2.488. Never had a problem with either. I think 4.0 was really needed by marketing to compete well with Rubicon rather than anything else.
Fording depth 30" v 24". Either can be improved with snorkel of course.
Notwithstanding above mostly likely H3T would be more pleasant driving around with light load/crawling over stuff. I would be concerned trying to haul heavy load like camper.
H3T has only 1090lb payload. Even with lightest camper + 2 people in the cab + supplies you'll be close/over Max GWVR of 6100lb. You might be able to level your truck using helper air bags or something but is it really built to handle this much load? Over rought terrain? Towing trailer over rough terrain like you said will restrict you far more than marginally smaller approach/departure angles on bigger truck.
Going back to keeping your horses. How about Roof Top Ten (RTT) on your current rig. Sleeping out of snakes but might have to visit them if nature calls.
The numbers you quoted are without the off road package and 33" wheels. My H3T has the off road package but I'd upgrades to 35" wheels. With 33" wheels the approach angle is 38.7 deg, departure 30.1 deg, breakover 21.1 deg (you got me there), and minimum ground clearance is 10.2". I don't know how they define running ground clearance. I also don't put any faith in RTI. I've never seen an RTI ramp on the trail. RTI is important to people without lockers because they have to keep the tires on the ground. With lockers you have traction even with a wheel or two in the air. Hummers lift wheels off the ground a lot but they still get through. The lowest point of the H3T is the shock mounts, so I replaced mine with low profile shock mounts which increased the ground clearance to 10.5" (to the differential) and going to 35" tires increased ground clearance to 11.2".
The 4:1 transfer case is very useful for crawling over rocks, climbing steep hills and also for descending long steep grades. You manually downshift the auto trans and it reduces heating in the brakes.
As I said before I just love my H3T. That is the main reason I'm not considering alternatives that involve replace it. Towing it behind an RV would be OK.
The weakness of the H3T is the load carrying capacity and putting a camper on, even a small lightweight camper is going to put it over the weight limit. I would probably upgrade the rear springs, but the weight is still a concern.
I thought about a roof top tent on the H3T, but my would still have to go down to ground (snake) level to use the porta potty.
Which part of Falcon is too wide? seems like you have 48" between wheel wells and 54" gate. That's plenty to fit I think. They have picture of Falcon in Chev Colorado. Or am'I missing something?
I attached a PDF of the Finch. The Falcom is the same width but shorter in length. My issue is the 51.5" width of the box that forms the base. My truck measures 50.5" inside the box. I don't understand why Hummer made the inside of the box narrower than the Colorado & Canyon.