Some UW photogs ARE experimenting with using a "video" type light for stills. The advantage is that you have a great light to use for other things, and when you use it for photography, it is easier to "model" that a flash. You can instantly see changes in the lights intensity and direction without having to take and review a photo.
The downside is that you need a BIG light or better yet , multiple lights......$$$$. Also almost no light on the market can keep up with the possible light output of a strobe.
The battery reqirements of the light are also much greater than the strobe, as it is left on , while the strobe is on for only a split second at a time.
Both are good option, but you will have to work withing the limitation of either one.
Personally- I don't care for flash photography in any form - I think you need $$ and Professional skills to pull it off. I prefer natural lighting, or a daylight balanced artificial light.