Self Types are an extension of the Calculus of Constructions  that allow the language to express algebraic datatypes encoded through the Scott Encoding. The Scott Encoding provides one the ability to pattern-match in
O(1), which is one of the main motivators for the inclusion of inductive definitions on CC. Yet, Self Types are make for a much simpler and elegant base theory, and are seemingly no less powerful.
Do Self Types, under a theoretical point of view, make CIC obsolete, or is there still some aspect on which CIC is favorable in relation to Self Tyes?