Soapstone is softer than alabaster, so it's a bit easier to work. It sands very quickly as well.
Lots of different colors available depending on where your soapstone comes from...and the color can change dramatically when a finish is applied (oil, shellac, lacquer, etc).
You can see what the "finished" color will likely be just by wetting the stone. Sometimes the dry piece will look pretty boring, but once you wet it, the color is surprising.
Other pieces of soapstone have shown the opposite results...interesting color/grain when dry but solid black (or very dark) when wet/finished.
Here's a soapstone shaving brush I made late last year as a Christmas present:
Turned quickly, sanded quickly, but it makes lots of dust along the way (likely very similar to what you had while working alabaster).