My 5 cents man- Egg whites are a
slow digesting protein. You need Fast digesting proteins like Whey right after workouts and first thing in the morning. Egg whites are more beneficial when taken as the last meal of the day an hour-2 hours before bed or anytime throughout the day as a meal. What egg whites does is, it builds up a kind of molding on your stomach liner and it will take in little bits at a time and feed your body protein at a steady pace.
Whey Protein is designed to breakdown all at once and go straight to the muscles with the nutrients they need to rebuild. Casein protein is also alot like egg whites. So my advice (especially if you weight train) use both.