An eccentric cone is similar to a concentric except the minor opening is moved out to the edge of the cone. Eccentric cones typically don't have a knuckle or a straight flange, but they can be polished for sanitary applications.
The major advantage of eccentric cones is the ability to place the outlet closer to where you want it. For certain applications, four tanks could all have their outlets near a central location or the position of the minor opening could make the outlet easier to reach.