I eat both.
I like yolks for all the nutrition and the taste.
But sometimes, I don't need more fat, and want only the protein, so I have whites only.
In other words- it depends on my "diet" for the day.
For breakfast I drink my coffee with half and half, and I have it with a chocolate protein pancake, which I cook in coconut oil.
There's a fat in the creamer, in the oil, and in the baking cocoa. So for my pancake I use egg whites, because I don't need more fat, but I do want and need the protein.