On my NX4510HST/cab, I have the big Titan turf tires that Kioti offers. Even when the ground is wet (but not spongy), I barely leave tracks on the lawn and paddocks. If turf tires would work for your other tasks, I'd say you wouldn't notice much difference between those two tractors on your lawn.
I'll disagree a bit with Dieselbound's comments on surface contact area. I think we have to distinguish between ground pressure (which I would call "point load') and the overall friction coefficient the tire surface imparts. They are related, of course, but can be very different depending on the ground condition and tread type. Given the same weight over the axle, an AG or R-4 tire can assert a greater ground pressure per square inch at the points of contact (technically measured and expressed as "ground reaction force"). Yet, because less tread area is making contact, there can actually be less overall traction. A good example is on hard-pack snow and rough ice. I plow a fair amount of snow on an access road and residential driveways. The turf tires (R-3s) have considerably more traction than R-4s in those conditions, and way more than R-1s.