The H3 is nothing more than a re-badged Chevy Blazer/Colorado with some custom body panels and Hummer-like interior touches. It's got a dinky engine to boot. (The H2 is a re-badged Tahoe, by the way.)
Neither the Tahoe or the H3 are at the top of the list for big SUVs but the Tahoe is far better than the H3 -- and the H3 is really a mid-size vehicle. If those are your choices, get the Tahoe. It has more room, better hauling capacity, is more reliable, and handles better. Blind spots are a big issue on all Hummers, another negative.
Any body-on-frame SUV will have safety issues. They are much more likely to roll over if driven improperly. Drive either as if it is a truck -- they both are -- and you'll be OK. But thrash it around like a Mustang GT and you'll be on your roof in short order.
Better choices than either, according to Consumer Reports, include the Toyota Sequoia or the Ford Expedition. The Toyota is the hands-down winner for quality and reliability and competes well with the H3 for size though is a bit smaller than the Tahoe. The Expedition beats any GM for quality and reliability and is competitive with the Tahoe for size and carrying capacity.