Have one, have had it about a year now. 2013 Diesel with 74k miles. Just towed 616 miles round trip from DC to Pitt Race and back with my 20' enclosed trailer doing 65-70 mph in the mountains of the PA Turnpike. It's a properly miserable tow and the Cayenne handled it as well as a half-ton truck does. My trailer is aluminum and loaded up with my E36 325is Spec3 car, weighs about 6,800 pounds.
You have to be mindful of tongue weight – most people towing want to just slam a trailer on the hitch and never think beyond that, which is not how to safely tow with any vehicle, let alone an SUV of this size. I've measured mine and it's within Porsche's specs. I use weight distribution and sway control on my hitch (Blue Ox). Porsche does not allow this per the manual because in Europe, it's not allowed at all. So, they don't test for it and thus don't certify it. But, with WD/SC I had 18-wheelers passing me and precisely zero movement at 65+ mph.
In 85-95° temps going up the Turnpike's grades – Wikipedia says they are a max of 3% – I could mostly maintain 65 mph. Slowed down to 55 or 60 a few times as oil temp was getting hot.
The TDI is a reliable engine with a few known issues. They develop an oil leak from the lower timing cover, and it's an engine-out service (per Porsche) to fix. Dieselgate gave these an extended warranty that lasts 10 years, 120k miles from date of first sale and it covers the entire long block - including leaks - and all emissions gear. Mine being a 2013 means the warranty expires this December, but any slightly-newer model will have the warranty for a bit longer. They sold them through model year 2016. This work was over $12k billed to Porsche N.A. and $0 to me, and they replaced every single seal, nut, bolt, and part they could while the engine was out. I got a new oil pump just because they don't want to pull the engine a second time, for example.
Once "the big re-seal" has been completed, the TDI seems to be durable so long as you drive it hard and don't just putter around town. Towing counts.
Transmissions on these are an 8-speed Aisin torque-converter automatic, not unlike what Toyota uses. The 958 generation Cayennes have transfer case issues but the Diesels used a different model that doesn't fail. Mine has the basic shocks and steel springs - it is rare to find a diesel with PASM + Air but you can.
I find them to be, frankly, astonishing vehicles. There is no other SUV on the market, new or used, that can tow a 20' enclosed trailer at 65 mph and immediately do 65 mph on windy back roads after unhitching said trailer.
Oh, and I got 14 MPG towing this past weekend and can do 32-34 MPG unloaded.