The Hummer H3 is a real off-road machine, and this is the main issue about this vehicle. Have you ever seen a tank winning a race? So there is no need to talk about acceleration here.
The Hummer H3 does great at everything it has been built for.
Mine has a manual transmission, and yes the towing capacities is 3500 pounds instead of 4500 for the automatic transmission, but there are reasons for that. First it is a clutch issue, because the truck will take whatever you are giving to it, compared to the automatic transmission that will take only what it can. Nothing can prevent the driver from shifting into 5th gear with a manual transmission, which is an overdrive, even if you are towing an heavy load, a thing that the automatic transmission won't do. So the hauling capacity is rated that way to protect you from exceeding the truck capacity.
Now let me tell you something, I'm pulling a 23 foot boat on a tandem trailer with my 2006 Hummer, which is equipped with a manual transmission. Of course there are brakes on the trailer, and I don't have any problem with it, but again you have to use your head, go easy on the throttle and do not try do break any speed records, and the truck is more than able to do that.
By the way, I've own 4x4s since 1976, and I still have my CJ5 Jeep, which is a 1974, and it is still in excellent shape. I also had a 1986 Chevy Blazer for over 13 years, and believe me, that truck was pulling a trailer almost every day, and it was still running great when I sold it, so my point is if you operate your truck properly with the right on time maintenance, it will keep up for a long time.