Strobes stop motion, including inadvertant camera or model shake.
Strobes let you use a higher aperture giving you more DoF allowing for your focus to be slightly sloppier.
Strobes don't (or atleast shouldn't) bake your model or make him/her sweat.
Strobes use less energy and are less likely to pop a breaker even when used in volume.
More accessories are compatable with strobes.
Strobes are daylight balanced.
You can move strobe heads around while they're on without asbestos mittens.
Strobe modeling lights aren't as bright allowing the subject's pupils to open up.