since both KYBELLA & AQUALYX contain deoxycholic acid, what's the actual difference (except they're used in different countries)

In the United States, Kybella is the only product FDA approved for chemical lipolysis before the chin.  It would be your only option in the United States.  

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 (a.k.a. Belkyra in some countries) is deoxycholic acid.
Both work in a similar fashion, and are effective at effecting permanent fat-loss in the treated area.

Kybella is your only option here in the United States. It's the only product with FDA approval to treat submental fat. Kindly,Kouros Azar

Kybella is the only FDA approved injection for destroying the fat (dissolving it) permanently under the chin.  The other option is the Coolsculpting (mini applicator) to permanently destroy the cells.  Please consult an expert.  Best, Dr. Green