Interestingly, eggs add smoothness up to a point. When that point is reached the eggs will act as a drying agent. If you use too many eggs you will have a souffle. If you over bake that souffle you will have something more like sweet ciabatta bread than a cake. read more
If you add only whites and beat them first the cake will be taller and have a lighter crumb, like angel food cake. If you add only yolks, the the color will deepen and the cake will be more dense. If you add whole eggs the overall change will generally be a more dense cake because most people won't separate to increase air volume in the batter. read more