I guess your question is about constant phase element (CPE) and capacitance (C) in electrochemical impedance spectroscopy. C is a specific case for CPE (when n=1). Typically, compared to C, CPE is more general in describing electrode materials consisting of rough surface or whose behavior deviates from an ideal capacitor. This paper is a good reference:
Article On the physical interpretation of constant phase elements
It is always better to use CPE as the electrochmeical systems are never pure capacitors. CPE gives the flexibity of both resistor and capacitor properties which is the actual case.