I asked about that at my last admission and was told there is no difference in priority or ‘service’. Maybe it happens behind the curtains but not as publicly stated/admitted policy. Conclusion, using private health in a public hospital always benefits the hospital and only might benefit the insured patient - with no way to tell about the latter. For elective surgery there is a difference in that one picks their surgeon whose office arranges matters. In my limited experience the private system prefers private hospitals where/when available.
A germane older topic
