Alot depends on the size of and health of your tank. For many many years I kept healthy tangs in a reef tank with their only food being that which the tank produced. In my outdoor tanks I keep an assortment of tangs, whose only diets is what the sun grows. The fish are fat, healthy and colorful off the all algae diet.
But you have to have a tank which is producing enough food to keep them plump and happy.
Having kept tangs that feed off of just algae, feed off of the best of supplied foods, and fed just pellets and romaine - I can't say that I can tell you that there is any difference between the fish with different diets. The best looking fish by far, are those out in the sunlight feeding what the sun produces. But having kept an assortment of tangs for up to 15 years on pellets and romaine - For those using that method I don't think they are doing anything wrong.
Dave B