Well the two advertisements I've seen for comparison for the Hummer H2...
- Kids soapbox Hummer replica goes offroad and wins a soapbox derby. 2. Hummer riding "offroad" with Regis and a Italian model riding in it while it's on the deck of a cruise ship.
Never seen a Hummer commercial where the Hummer is actually off road (under it's own power).
Jeep commercials sometimes show the product actually doing off road stuff. I can only guess that the Hummer (at least the H2 version) isn't really very good off road (or they'd show the product in that environment...he?!). Jeep's marketing folks are playing off the Hummer commercials (see we're "trail rated" since see we're actually showing our product on a trail!)