I've been able to drive vehicles with and without (granted, they're two very different vehicles, Landcruiser and my 4Runner) and I think the main advantages of the KDSS are flatter cornering on road, and your suspension will have a little less resistance to flexing when off road. I've got the TRDP because I've got a long history of modifying vehicles and I wanted to buy a vehicle that had enough "mods" on it to keep me from modding it myself. So far, the only things I've done are rock sliders and went to 33" BFG KO2's. I know the Landcruiser isn't a 4Runner, and this might not be a fair test, but I've been able to feel how the KDSS keeps it more balanced in corners and yet lets it still be very good off road. The only advantage of the Pro vs the Landcruiser with KDSS is in high speed stuff from what I've been able to personally test. On our local baja track that is disguised as a main road (our roads are truly awful with washboard crap and everything - seriously, some of the trails I've seen people get stuck on are smoother than these roads) my 4Runner rides smoother, but only when going faster. At the 35mph speed limit, the LC is smoother. But, when you take them both up to 60-70 (not advised as it's double the speed limit) the 4Runner becomes smoother and more stable. 99.9% of the rest of the time, you can tell the KDSS is a fantastic system. If I were in the market for a 2nd 4Runner, I'd 100% go with one that has KDSS. Off road on trails, with equal tires, you won't notice any difference at all. They'll both go all the same places with the same ease. On road is where you'll notice the main advantage. I only bought the Pro model vs the Trail (Off Road) because I didn't want to mod it as much as I have other vehicles in the past. My wallet is happier, and I've got a vehicle that I am thrilled with and suits the stuff I want to do with it. You will be thrilled no matter what you buy, and whichever one you get, you'll eventually feel like you picked the perfect one for you regardless of what it is. They're all 4Runners, KDSS or not, Pro or not and they're all fantastic haha.
In terms of ground clearance, that's all gonna be in your tire size. The larger lift will only allow you to clear bigger tires, but bigger tires will lift your pumpkin and everything else off the ground. I seem to be one of the few people to fit 33's without any rubbing whatsoever, but with some very minor adjustments (if any, you could be lucky like me), you'll be able to fit them onto an Off Road model too. There is a whole other post regarding that which is easy to find, but I'll send the link if you need it. In terms of wheel travel, there won't be a difference EXCEPT that the KDSS will likely be a little less restrictive. KDSS basically behaves like a very thick sway bar on road and a very thin one off road all without having to change it out when you hit the trails. That's the simplest way to put it. The Pro has a very thin one all the time. I don't mind the added body roll, but coming from low sports cars, I feel like a truck based vehicle should roll more than what I'm used to, so it feels normal. For the trails you posted, you likely won't notice any difference at all vs a Pro and one with KDSS.
Whatever you get, post pics! Remember, you can add the visual stuff on the Pro very easily, so don't let looks be a factor. It really is just a Trail model with some black accents instead of silver and a different grill in terms of looks.