Am looking at booking Aus-Akl for September, 2019. Am getting flights for both AA and for AA/Qantas, with same or very similar flight times, departure times, and routes, but different prices (for Premium Economy), and, of course, flight numbers.

Are these really different flights, or is AA just neglecting to indicate that they are code share?

Other than possible price difference (which may be that the AA flight shows flexible, but AA/Qantas shows nothing), is there anything special to recommend one carrier over the other? We have no status, are retired and very flexible with travel plans, and will be using a new AA credit card regardless of carrier.