adhoc, this is my 2 cents worth.
I think the general view is that Aus has more stable weather than NZ and there are more options for cross-country navigational flight routes during your training. Aus is globally recognised as a leading flight training centre.
Bini is not CRICOS accredited, which means they cannot organise a student visa for you. However they do accept international students who will have to enter the country under tourist visas which last only 90 days (you would have to travel between Indo and Aus several times) and that is not ideal from your point of view. Besides, Bini is not geared towards ab initio training as they only have one or two full time instructors who are available on duty (others are part-time only). Bini's expertise is really multi-engine instrument ratings only.
If you are interested in training at Moorabbin Airport (Mentone, same place), I would suggest someone like Moorabbin Flying Services. It is CRICOS accredited (no problems with student visas), has many full-time instructors training ab initio, a large proportion of international students, and very new aircraft (just a few years old compared to most other schools around 30-40 years old). You will find them very professional in their approach to training and customer-oriented so no one feels left out.
Moorabbin Flying Services