I have had both the Michelin and the Continentals. Mine are summer performance tires, not all season. Both are very equal. I would have stayed with the Michelins, but the size I need were out of stock, so I went to Continental. Both do great in rain, and on my cross country drives, I always have some rain. I have had them in freezing conditions, and they get rater hard until they warm up some.
I just drive it like it is not a sports car until the tires warm up. For real winter weather, with ice and snow on the ground, yea, you want all season tires.
Jay Leno says that the Michelins always seem to take less weights to balance the tires as they are very round.