Take this for whatever you think it's worth. I've driven nearly 2 million miles for work in ND, SD, MT, and MN. FWD cars, AWD SUV's, and on personal time, a full-size pickup (3/4tn diesel for the last 14yrs).
Dedicated snow tires like a Blizzak are exponentially better than anything labeled M+S, including 3-peak. It's not even close when it gets slick. The true difference shows up when you need to slow, stop, or turn. 25-30K Mi max out of a set, maybe a little more if you put them on a 2nd set of wheels and run them winter only. The difference must be experienced to really appreciate it, words don't do the difference justice.
Studs on pure ice are still the best, but, the trade-off is that the same tires with and without studs on the same vehicle, studs don't stop or turn as well on dry pavement.
3-peak rated tires have made AS, AT, and M+S tires WAY better on ice and packed snow than they used to be without giving up longevity like a dedicated snow tire will. Because I run a lot of gravel in my personal pickup, I have Nitto Exo Grappler 3-peak tires on it. On packed snow/ice they're better traction than BFG AT KO/KO2, Goodyear DuraTrac, Nitto Trail Grappler, or Nitto Terra Grappler. I've had all of these tires on my current pickup ('11 F-250). A buddy had Falken Wild Peaks on a '10 F250 that I drove 3K-4K Mi with on different hunting trips and they aren't as good as the Exo's either.
I've had dedicated snows from Bridgestone (Blizzak), Goodyear, Cooper. The Blizzaks are noticeably better at stopping and/or turning than the Goodyear Winter Command. On 2 different vehicles I was able to have both the Goodyear and Blizzak on them, the Blizzaks are so much better than even my wife who's fairly oblivious to handling noticed the difference. The only other dedicated snow I'd consider beyond Blizzak is the Nokian Hakka's. That's based on a couple of folks who drive about as much as I do having good luck with them across multiple vehicles.
Again, take it for whatever you think it's worth.