When my ZT had oem tires, I had two complaints...
1.) When I had to mow straight down a grade, stop, and back up (like mowing up to a ditch or pond shore) too many times I did not have enough traction to back up and then I had to get the real tractor out to pull it back to flat ground.
2.) It will travel sideways along a slope very well until it was time to maneuver around a tree and on the downhill turn it would slide down the hill a foot or two past the tree leaving a minor skid in the grass and I would have to make a second pass to trim the missed area on the downhill side. Forget about mowing with dew on the grass no matter how much ease was used into the zero turn. It became a sled.
Now that I have ag style rear tires I have one complaint...
When you loose control, even though it's a lot less frequent, the skid in the grass becomes a rut. BUT it's a lot safer and gets out of wet and downward facing predicaments more on its own.
My bias for ag tires really only applies to the rough terrain that I own. I would say that 80% of what I mow (2-4 hours a week) has slope to it (lots of trees) and a creek that runs through the middle.