While Chris is quite correct, one of the primary advantages of using a studio strobe would have to be the flexibility it can offer you.
With a greater intensity of light - usually switchable in terms of power output - you can have a greater variety of apertures to play with, thus giving you greater control over your DoF than might be possible when using continuous light.
Also, the lower intensity of the continuous light might force you into using a tripod where a flash might permit handheld images.
And if you're using live
models, you might need to consider that the heat output of continuous lighting might cause your
models to perspire. That might, or might not, be desirable from the POV of the image that you're trying to make, but it's still something to be considered.
Certainly, for studio tabletops and still lifes, I think either are very workable solutions, but once you get into people shots, I think that the strobe starts to have a slight edge over continuous lighting.