I wonder how much modification you would have to do to the Cayenne to make it really off-road worthy. I suspect you'd need a lift kit and new wheels at least (all the photos I saw on google showed low profile tires), which would add to the price. And it looks like it's already an $80k vehicle, so not exactly a "small price."
I've never been a huge fan of the Discovery, and the version you mentioned looks worse then a Subaru Forester, but it's much less expensive, and ready to go off-road right off the lot with decent clearance and wheels that can handle real all-terrain tires.
I do a fair amount of off-road driving, often on alpine jeep roads that require a pretty capable vehicle, but I'm not fancy and I don't care if my car has a prestigious brand name. I am on my third 4Runner, and when it's time for my next vehicle, it will probably be a 4Runner with the TRD trim. The new 4Runners aren't quite as good off-road as the ones from 20 years ago IMO, but they are still very capable, and obviously the Toyota reliability is second to none.