My experience with tires over the last 45 years:
R-4's SUCK They are on my mowing tractor, because, as was mentioned above, "It's all they had." They are hard, stiff, and give a really crappy ride.
R-1's in summer ROCK! They tear up the yard LESS because they do not spin like turfs will trying to crawl over a piss-ant hill. 15,000 pound farm tractors, pulling wagons and equipment even heavier, driving across the lawn didn't hurt it, it's DIRT AND GRASS for cripes sake, not the carpet in your living room.
Turf tires RULE in winter, with chains of course. As was mentioned above, where the ground freezes and one is running on frost and ice, rubber slips, I don't care what the shape of the rubber is. I've sat on 10,000 pound farm tractors going nowhere fast as the lug tire's rubber just spun on the ice. On smaller, garden to compact tractors where the chains are run fairly tight to stay on, the crosslinks work in between the lugs and do jack squat, turf tires work far better on these tractors. On larger farm tractors, where chains are run loose to "fly away" as much as 3"-4" from the tire, R-1 type ag tires will work.
My "ideal" is R-1 lugs in summer, turfs with chains in the winter, but I'm stuck with R-4's because "They are what everyone wants." B.S. on what everyone wants, I'd rather have something that WORKED.