Juri wins 8/10 times.
Even starting 100 feet apart, Juri can easily close the gap. As shown in the end of the SFIV OVA she's had her limiter removed so there's no time limit issues regarding the Feng Shui Engine, and she won't hesitate to activate it once she views Azula as a credible threat. In the OVA, Juri was able to stop Chun Li's kikosho with one hand (a technique capable of KOing regular humans with ease in the Udon comics), so Azula's lightning will likely hurt but not do any significant damage. Once again in the OVA, Juri managed to blitz Guile, Cammy and Chun Li when she got serious, and proceeded to one shot all of them.
I feel like Azula could definitely do some damage with her fire bending, but Juri gets way too much of a physical boost from her engine. Plus Azula is a total glass canon and if Juri lands a solid hit then she's done for.