There no advantages/disadvantages one over another. CX is not a standalone ASA, but a module (hardware or software), wich complements normal ASA with some extended function, as Application Visibiltiy And conrol and web filtering. Technically, CX is module, wich allows the ASA perform functions, usually done by cisco ironport VSA.
Traffic, after being filterd by "normal" asa is redirected to CX for further inspection and policies application.
You can see session on ciscolive365.com regarding CX or just google what it is. And, as I said, you souldn't compare them.