I have had both the Bridgestone Blizzak and the Michelin Arctic Alpin snow tires. The 4 Blizzaks I had worked excellent, I would say you can't go wrong with these tires. They give the best damn grip in deep deep snow, and they do perform good in icy conditions. Worth the money, however I now have a set of 4 Michelin Arctic Alpins because I have a different car now. The Alpins are good too, perhaps slightly lower grip than Blizzacks in deep snow or on ice but they won't wear out as fast as Blizzacks. Alpins also give a smoother and quieter ride that Blizzacks, and perhaps better gas mileage. I have used my Alpins for two yr and I can't see any wear on them. Blizzacks will wear 30% faster in, due to the outer 40% of tread being made from a softer compound so it will grip better. But when it is worn down you will have less traction than an Alpin.
Get 4 rims also, cause when you switch tires from rims every yr the tire gets dammaged (around bead). It happened to me(had low profile tires). Overall, Michelin and Bridgestone make a good tire, main difference being smoother, quiet ride from michelin, and rougher, noiser, faster wear, but slightly better grip with Bridgestone(truck like ride). If you plan on keeping your car for along time buy these brands, with rims, if not, it may be cheeper to pay and have your tires switched, but tire dammage is possible if they are low profile. Hope this helps.