Yes, there really is no comparison between snow tires and all seasons that are sutiable for snow or even performance winters for that matter. Dedicated winter tires provide superior grip by a reasonable margin. The most gains come from ice grip where compound and siping yields big dividends.
Just because you haven't driven on real winter tires doesn't mean you couldn't gain from doing so. I too spent a lot of my earlier winters on all-seasons. I too didn't realize the benefit of true winter tires. Heck, back when I started driving there wasn't really winter tires to speak of. I live in an area that can't use studs, so the only options were all-seasons. Winter tires have really blown up in recent years and so has tire technology. Newer tires are lightyears above older tires and winter tires have grown as a genre quite significantly with its own performance levels gaining significantly.
As a rough comparison, winter tires give you the same benefit as dedicated summer tires when deviating from standard all-seasons. The gains are moderate for the surfaces they are designed for.