Dye won't control filamentous algae. I'll come from a slightly different angle that what Bill explained.
Dye prevents the sun's UV rays from penetrating the water column. That's what prevents (not control) plant life from growing. From a "productivity" perspective, we need sunlight to grow plankton. Plant plankton feeds the animal plankton which feeds slightly larger insects, threadfin shad and filter feeders. Those insects feed small fish which feed larger fish which feed bigger fish.
So, people who are interested in natural production of fish won't use a dye. People who's fish depend on fish food often prefer dye in order to minimize risk of filamentous algae. People with less interest in growing as many fish as possible often use dye, in an attempt to keep algae away.
