I have 245/75/16 Cooper Discoverer ST/C's on my truck, and I was pleased with their performance last winter. I found they were about as effective as a cheap snow tire, and there would be little reason to use another set of snow tires. Where they don't work as well is on ice. Even cheap snow tires should have a silica rubber compound, which remains more flexible at low temperatures and works better on ice, slush, and cold pavement.
Regardless, I had no trouble at all serving as recovery crew during a Pro-Rally up in Quebec in Febuary. That required me to maintain pace with the rally, and I had no problem at all. Never did I think the tires were a liability.
From the cheap winter tires, you step to a premium conventional tire like the X-Ice. This has a good rubber, with a sophisticated tread pattern with huge amounts of siping. These will give a marked improvement on ice, hardpack snow, etc. They still won't likely give you better traction if you're just trying to paddle through deep powder.
And then you have Blizzaks, which are in a whole other league. They offer perception-altering levels of grip on ice. After you've experienced Blizzak traction, it's hard to want to go back to regular tires. The problem with Blizzaks is they are pretty terrible on dry pavement.
Lately I have been running Dunlop Wintersport tires on my passenger cars. I find these offer good snow traction (still only the same as A/T's) and decent ice traction, but more importantly, they offer fantastic pavement traction, much better than other snow tires, which is important for the other 80% of the time when the roads are clear.