I can agree with a lot of what has been said, but the grass / soil at YOUR house has a lot to do with your success with different tires. So do things like not removing the loader or using 4WD and cutting sharp turns.
First tractor I had here was an old 2WD Cub LoBoy with turfs on the rear and worn out ribbed tires on the front. With any dew on the grass it slipped on hills and the front wheels drifted when turning sharp. It was pretty easy on the grass.
Second tractor is a little Ford 1210 with R1's. It does OK unless the ground is real soft but does leave more of an impression in the grass. Still have it and it was the only tractor I had from '92 till '02. For a period of time I kept about 7 acres mowed with a 5' Caroni RFM.
From '02 till early 2012 I added a Kubota
B7500 with a 5' Landpride RFM. It had R4's and was a little easier on the grass. For mowing, the loader was always removed for two reasons. Without the loader the tractor was easier to trim around things and the front tire didn't mark the lawn much at all on turns. It did have loaded rear tires.
In 2012 I sold the
B7500 and bought an
L3200. This has a 6' Landpride RFM and loaded R4's. Again, the loader is in the shed when I'm mowing. This has been the best one of the bunch. It's nice to operate and marks the lawn less than the others did. We have a creek in the front yard and sometimes it makes the front of the place into a big pond. When that happens, the farmers upstream donate topsoil - in the form of what looks like up to an inch or so of brown yogurt. The bigger tractor leaves the least imprint when I get too impatient to wait for the ground to dry.
Here are a couple shots of the front yard (looking in two different directions). One "wet" and the other just after I finished mowing with the
L3200 last week one evening.
