This is a million-dollar misconception. Let me explain to you why.
I have been under the same influence (in 2006) and bought Land Cruiser - thinking, it was a king of desert as all desert safari companies are using it. After the first few drives realized its boat size was heavy and long and not practical for any good dune bashing. Why Desert Safari companies use it because it's the most forgiving and economical car for their daily business - which require a 15 min - 30 min desert trail in a 5 km radius for tourist to show sand splash, few sideys and moderate climb at sunset point. This train track route is miles away from what weekend offroaders do - explore, push the limits, and cross the desert from one side to another.
Fast forward two years, after seeing so many Patrols flying thru the dunes - bought a SWB patrol in 2008. It was much better than LC but still unable to fly through anywhere. The simple reason was Patrol used by local and racers boys has been heavily modified with a buffet menu of 400 HP - 800 HP - 2000 HP depending on how deep your pocket and wasta. Now, if we buy a new car and are scared of voiding the warranty, we have to limit our reach and find peace somewhere in between. Why ppl love Patrol to be modified is the core reason that it has a huge engine bay with the smallest engine size, that can fit a hell of a mod, turbos, fans, and headers and still disguise as regular Patrol.
If you really wanna base your offroad car purchase, go to any offroad club drive starting point and see you will find:
75% cars with a mix of Wranglers, FJC, Patrol (SWB) and Xterra (older model)
20% Land Cruisers, Patrol Safari LWB, Prado and Pajero's
5% Patrol Y62, Grand Cherokee, Discovery, Liberty, Fortuner etc.