I can't really speak to the GX vs. Hundy debate, as I've never driven either, but I'll just add another vote of confidence for the 5.7 Tundra. I'm on my 2nd one. Traded the '07 CrewMax SR5 (first year of the 5.7) in for my current '15 CrewMax 1794 Edition. There was nothing wrong with the '07 at 100k miles. I just wanted more bells & whistles. The CrewMax has a TON of interior room for people or stuff, but not really both, since it's a pickup. If you get a good tonneau cover or bed cap, problem solved.
I've towed my 4Runner or 40 on a trailer many times behind it. Total weight, including camping gear, tools, and spare parts is just shy of 14k, as measured on the CAT scales. Since the Tundra is around 5,700 lbs., that makes my cargo + trailer combo around 8,300 lbs. Several hundred pounds of that is usually camping gear, coolers, etc. in the bed. Towing capacity is stated as 9,800 lbs., so I should be just fine.
While I may get a weight distributing hitch at some point to help out, it tows great. Power is not an issue. I've towed up Old Fort a few times and I can go as fast as I want with no issue. The only downside is fuel economy. I get around 10 mpg towing. Compared to other gassers, that may not be horrible, but compared to a diesel, well......it's not good. Of course, diesel costs more, but I still think you'd come out better, cost-wise.
I almost bought a 1st Gen Sequoia as a tow rig before buying the '07 Tundra. I saw a couple that were REALLY nice, but I would've been right at the towing capacity, so I test drove a Tundra and my decision was made.