I don't think it's as simple as which can push more snow. Each has a place where it excels over the other. If I was going to be clearing a parking lot I probably would opt for the SS over a tractor. But for a driveway I would rather have a tractor. Attachments for tractors are usually cheaper and with a tractor you can have a plow or snow blower on the front and a pto driven sander on the rear. On wide open places like a parking lot it wouldn't matter but on a paved driveway where you'll be making tight turns and you need chains the skid steer will be more likely to cause damage. But since every driveway is different it's hard to make a general comparison.
Same weight and same tires, chances are they will push about the same amount of snow. Most likely the tractor will be lighter so it will have ballast in the rear to get the weight the same. That'll mean the weight distribution would be close to the SS. About the only read advantage one would have over the other is the tractor will be two wheel drive (one front and one back) unless you push the diff lock then it'll be 3 wheel drive. The SS will be 4 wheel drive until you try to turn.
I did not think about all 4 wheels on the ss will pull.