There are lots of reasons why you might prefer one over the other.
1) Flash is (generally speaking) instantaneous - nothing freezes the action (and avoids camera shake) as well as high-speed electronic flash.
2) Portability - unless you have a large studio setup, it's easier to carry a flash than a set of lights.
3) Spectrum - It's easier to get an equivalent of daylight (generally speaking) from a flash than it is from most continuous light sources (apart from the sun itself).
4) Intensity - flashes ARE bright, and even in a studio setup it's possible to use smaller lens apertures (and hence get (usually) sharper pictures).
The downsides of flash are:
1) Without a studio setup, you get harsh shadows.
2) Without a studio setup, objects nearer the flash are disproportionately brighter than object further away (inverse square law applies).
3) It's usually more difficult to "get the lighting right" if you can't make continuous adjustments to it while setting up a shot.
4) It leaves models with a rather glassy look in the eyes after being blinded several times.
Ray Dart (ex-studio photographer).