Reinforced is usually a thicker, stiffer sidewall, for heavier duty applications, like vans. It will make no difference to puncture resistance or susceptibility.Wonder if that's the benefit of 'reinforced' tyres. If so, maybe worth the money?
Some tread patterns are more susceptible to picking up objects, or holding small stones to give an annoying tick-tick as you drive. As the tyre wears, it is more susceptible to punctures. Having said that, my very first puncture was on a brand new tyre, after about 7 miles.
The innermost layer of tubeless tyres is a softer butyl rubber, that will try to seal small punctures. The object makes a small hole, and the hole in the rubber is smaller, so seals around the screw or nail. Leakage is slower, preventing a sudden complete failure. Screws are more common than nails, as the thread tends to grip inside the tread, so it can pick up on the first rotation, and get pushed in on the second. If when you park, it is sitting on it, you won't see it, and the air escape is too gentle to hear. If just a small screw, most punctures are repairable, but longer screws can bend inside, causing damage, rendering the tyre scrap.