To answer your question relevantly, there is no 'practical' difference between Kybella and Aqualyx.
Technically, Aqualyx is a modified compound of cholanic acid (which is ever so slightly different from cholanoic acid a.k.a. deoxycholic acid - if I remember correctly!).
Kybella...
You appear to be a great candidate for Aqualyx. Though a treatment may still not be FDA approved, that does not necessarily mean it is ineffective or unsafe. It can take years for a treatment to become FDA approved and it is a very complicated process. What you should be more concerned with, is...
They work by the same mechanism, as both are forms of the same active ingredient. Deoxycolic Acid is a molecule that occurs naturally in the body and helps us to breakdown and absorb fat in our diet. When injected into the fat cell, it causes it to breakdown and be absorbed...