Glazing pastry - Egg white or Milk?
Milk contains several components, most notably fat, sugar, and protein.  These all add to the browning effect when cooked at high temperature (proteins cooked together with either sugars or fats undergo the "Maillard reaction").  The browned bits do have significant extra flavor, but it does not taste like milk.

Egg white, by itself, is pure protein.  It is typically used in pre-baked ("blind baked") pie shells because the dense protein creates a water-resistant coating when it cooks, so that the crust won't get too soggy when a liquid filling is added later on.  Quiche is a great example of this application.  Like milk, the egg white will add no flavor of its own, just the flavor associated with browning.  Egg white is also used in low-cholesterol cooking.

Egg whites will brown some, but not as much as milk unless the pastry itself provides extra fats and sugars for the proteins to react with.  Egg wash -- beaten whole eggs, usually mixed with a little water -- is more typically used to get pastries to brown.