I always try to change all season (what a joke) to winter tires before first snow fall (November) and always have known that traction was much better but never compared those two in the same conditions.
However an ultimate proof came last Friday. Weekend before I was deceived by warm weather and thought the winter was over installing all season (Michelins) tires. Friday was the big lesson. Winter returned with a vengence, ice, snow, ice pellets, snow again. All seasons could not cope, no much traction, stability just so so, not that I could trust it. In a big hurry I was installing (reinstalling?) my winter Gislaveds and what a relief. Traction, stability have returned.