There are lots of threads on this, if you search for them.
Basically, all the light from a flash is produced literally in a flash, with continuous lighting the light is on all the time. Flash is therefore far more comfortable for live subjects, it doesn't blind them or make them feel uncomfortable. But although it seems to be far less bright, it is in fact far more powerful than continuous light, allowing smaller f/stops to be used, and allowing lower ISO settings.
This is why nearly everyone uses flash.
Personally, I'm happy to use continuous lighting for some still life subjects, but then I use a continuous light that is very powerful and which takes S-fit accessories, so I have pretty good control of the light. Most continuous lighting can't do that, and so it isn't possible to fit accessories (light shapers/light modifiers) which is a big problem, as it is the modifiers that make all the difference in lighting.