It's funny ... so many people seem to think that a winter tire is going to give them perfect traction.
You will probably not see a huge jump from an all-season to a snow tire. You will notice that it is slightly better. The more you drive though, the more you will learn your tires ability ... and be able to use the increased traction. The increased grip will really show itself in the more extreme weather, deep snow, ice laden roads, and extremely cold temperatures.
You will also want to look at the conditions you drive in ... frequently ploughed and salted town roads or the 'we don't plough our roads as everyone as 4x4's' type country roads. Obviously unploughed roads will show the biggest difference.
If you really want to compare ... wait until another good snowfall and put your all-season's back on.