While reading the answers to this question I had to disagree at some points. For example referring to @DavidR I don't think that Softshells are generally less windproof than Hardshells. Over the last years it seems that the manufacturers are mainly producing Softshell with Gore-Tex Windstopper membrane. I wouldn't say that those jackets are really that good, they just seem to be very promotable and consumers like the security of the 100% windproofness. One just has to remember that you loose breathability by this security.
The same with Hardshells where you increase the security against the elements at the cost of breathability. Additionally to being windproof they are 100% waterproof (at least 10000 mm hydrostatic head) and not just water-resistent (like Softshells). This last point is the characteristic classification in my opinion, though a strict definition doesn't seem to exist. The hydrostatic head is a measure for the water pressure which may be increased by a heavy load backpack. Thinking about waterproofness you also have to take into account the duration and intensity of the rain/storm. The value 10m hydrostatic head is just a matter of definition for the producers to promote their stuff as waterproof. But still, newer jackets with e.g. 20000mm hydrostatic head give you a bigger safety not getting wet. Of course the task of the manufacturers is to keep the breathability at a good level. For example the Gore-Tex Pro which was released a year ago has the same pressure head of 28000mm as the precurser version. However it is said to be 28% more breathable which is the key improvement and will cost you a good amount of money.
There is another, more traditional definition of Softshell which is referring to jackets without membranes, being very breathable and only resistant to water and wind to some level. For lots activities those jackets are matching very well. For example Arcteryx and Outdoor Research is defining Softshells like this.
Most of the times a Softshell is made from softer fabrics, it wears very comfortable and don't has the annoying plastic-like rustling most Hardshells have. Consequently Softshells have more mechanical stretch than Hardshells and tend to be warmer.
On the market there is not just one membrane for the well known Gore-Tex, some are typical for Softshells, like the Windstopper or the Gore-Tex Softshell. For Hardshells you still have a big choice depending on what you plan to do. E.g. for trail-running or cycling there are Paclite or Active Shell which are very lightweight with small package volume. Of course this comes with a lower durability of the jacket. There are more robust 3-layer-jackets with Gore-Tex Pro which are made for mountaineering or climbing (where rock contact is likely). In general those expensive jackets are designed for extreme environments.
Nonetheless there seem to be big differences how people define Soft- and Hardshells. You can read more on sectionhiker.com and on outdoor-gear-deals.com. In the last link they say for example:
Soft-shell (also written as soft shell and Softshell) is more of an idea than a category of clothing; it’s essentially a concept. Typically, the clothes labeled soft-shells are not waterproof, as they contain no waterproof barrier; instead they offer varying degrees of water and wind resistance, and a high level of breathability. They tend to be more abrasion resistant than comparable hard-shells, but also heavier and more expensive. Most people seem to prefer the feel and style of a soft-shell jacket; they’re more comfortable and quieter than a crinkly waterproof hardshell jacket. The soft-shell materials are generally stretchy, and this makes them a great choice for active outdoor recreation; climbing, skiing, etc.
I don't see how Softshells are more expensive or more abrasion resistant at all. Besides that I agree with the definition. But as you can see, opinions differ a lot.
So, to sum up my definition:
- without membrane: extremely breathable, decently wind- and water-resistant, very comfortable, stretchy (fleece-like)
- with membrane: good breathability, windproof, water-resistant, comfortable
- always with membrane: breathable, wind- and waterproof, sometimes very robust
- compared to Softshells generally not as warm and comfortable on the skin, because of a different (thinner) inner layer
Of course there are also wind- and waterproof jackets without membranes. Those are typically cheap and you will sweat extremely if you plan to do some kind of activity outdoors wearing this stuff.
If you want to buy a jacket you really have to think about the situations where you plan to use the jacket most of the time. A retailer once told me that producers plan to make a universal membrane/jacket with being absolute wind- and waterproof and still having a really great breathability (don't forget the robustness).
I think this isn't possible at all. There is no perfect jacket. Also the high-end items designed for alpinism (which will cost you 600€ and more) with Gore-Tex Pro can't be that extremely breathable like a Softshell without membrane. But of course they are really tough and will secure you from the elements very very well. They are designed differently (e.g. to get your helmet under the hood and to be able to reach your pockets while wearing a harness) and to increase the exchange of the steam they often have additional zippers in the armpit.
That all being said, I don't want to promote Gore-Tex at all. There are lots of other membranes, like from Dermizax (Bergans, Direct Alpine), eVent (Montane), Membrain (Marmot), Venturi (Schöffel), H2NO (Patagonia) or Sympatex (Vaude).