I have never been overly impressed by Azteks. I own an A430 which has a plastic body, but is otherwise similar to your A777. It painted adequately enough, although there was nothing particularly remarkable about it. It's main advertising claim to fame was ease of use and cleaning, which is a claim that I found to be unsupported by experience.
My Aztek's body died for no apparent reason after a short service life, in spite of my having followed all the cleaning and care instructions. Based on feedback from this board and others, my experience is hardly unique. They don't really paint better than regular airbrushes, they don't clean up easier than regular airbrushes, and their reliability seems suspect, and they re fairly expensive. All in all Aztek is an airbrush that I recommend against buying.
I have a Badger 200 NH, which basically replaced the Aztek while Testors was making good on their warranty. It is a single action version of the Anthem 155, and with it I found it easier to spray narrower lines than I could with the Aztek's medium tip. I never really got the hang of effectively using the Aztek's fine tip before abandoning the Aztek in favor of the Badger.
Having said all that, since you have both the Badger 175 and the Aztek, try them both and see which one works best for you. In spite of my own experience with Aztek, there are a lot of people who do like them. After really using both airbrushes, you might find that there some things you prefer do do with the Badger and some things that you prefer to do with the Aztek.