Way back when, soapstone stoves were advertised as nirvana - the best thing ever to come up the pike! I have to say that I frowned upon some of the early advertisements, because they made claims that were a bit unreasonable (this is 1979 I am referring to!).....BUT, the consumer satisfaction that has been evident in the field in the last decade or so has convinced me that these stoves are the "right stuff" for certain customers. I think the pros and cons have been laid out pretty well above and in other threads, as well as in our article which compares stove materials.
One reminder is that thermal mass can be obtained in other ways besides soapstone. A heavy masonry wall (interior) and hearth can act as a heat sink, soaking up heat for hours and releasing it after the stove goes out. Also, heat retention and storage is somewhat related to mass (weight), so a 400 lbs soapstone stove is not going to do vastly more in storage than a 400 lb firebrick and steel one...yes, there is a difference in heat storage capacity, but it isn't a large amount.
The moderation of heat during the fire seems like one of the better features of soapstone.
As they say, there is nothing new under the sun. Russian and Finnish fireplaces, tile stoves and even antique soapstone stoves have been prized for centuries because of their moderation of the heat output.