The type of fat used affects both the flavor and the volume or lightness of the cake. Oil makes the lightest, airiest, prettiest cakes, but in this particular recipe, using oil also left an unpleasant taste. Oil can be useful in smaller quantities or if there are other stronger flavors present in the cake.
Butter gives a distinct flavor that some people like and others do not. Margarine generally has a mellower flavor profile, so it is not as detectable in a cake and is my first choice. Whipping the margarine or butter with sugar gives small, even air pockets and a soft pleasant texture. Butter makes a slightly denser cake.