I hadn't weighed in because it seems like this question has been discussed to death several years ago, so it is sort of surprising to see it rehashed here. It also seems like people haven't tried or don't understand the softshell concept.
It has gotten more complex over the years, since now hard shell jackets are marketed as stretchy and soft shells as waterproof, so the differences have become less pronounced and harder to sort out. But if we think of soft shells as schoeller like fabrics I think we can make some general statements. Softshells are stretchy, close fitting, highly breathable, wind resistant and rain shedding, but not waterproof. They are generally heavier than a "hard shell" but are designed to be worn all the time and almost never carried. Part of theory of switching to a softshell is to carry an ultra light "hard shell" for emergencies that you don't wear (I haven't worn mine yet in the winter).
In my experience, for high exertion activity in the winter, like climbing, skiing up, or snowshoeing, there is simply no comparison: a softshell will be far more comfortable than a hard shell. Wearing gortex was a continual process of sweating and venting and unzipping and taking it off and then putting it back on. With my softshell, I can wear on the way up, sweat maybe a bit, and then wear it on the way down, warm, dry and comfortable all the time. If you bought something marketed as a "softshell" and you are sweating and clammy inside it, you may not have bought one made out of an actual softshell material.
At temps above 60f, softshells lose a lot of their advantage, since you may not need a jacket and may sweat in anything. My jacket is wb-400, and so is ideal for winter use. My pants are schoeller dynamic, so I find them too thin and too light for winter use, but great for summer, so I need a heavier softshell for winter pants at some point.