Egg whites or whole eggs?

Both. The yolk contains some fat, but fat is not the enemy - fat has a stigma attached to it from the decades of "low fat" advice that basically allowed the obesity and overweight levels in the U.S. climb so you can see how effective that advice was. Eggs are often hailed for their high quality of protein, but few people realize that these tests are with the whole egg. It actually loses value when you only eat the yolk. The yolk contains nearly half the protein, fats, and healthy antioxidants such as Vitamin E. Eggs from free range or grain-fed chickens are superior in quality.

Traditionally, the yolk was shunned for cholesterol diet, another old myth that is dying hard - for more information on why you needn't worry about the cholesterol in egg yolks, read this:

Harvard Article