Hi!
I actually have friends in both USYD nursing and UTS nursing and without a doubt, it's UTS. This is recognised by both the students there and those in the nursing field in general. UTS nursing offers clinical placements for first year students and overall, prepares students for the work environment as they prioritize practical skills over theory - which is crucial for any career in the medical field.
I also have a few friends in USYD nursing who chose USYD for the prestige/university name and for their parents but they themselves also agree that UTS nursing students are provided with better facilities and staff because UTS nursing is one of the university's more reputable and highly-regarded courses.
In regards to your decision on post graduate medicine, I just want to say that post graduate medicine is still difficult to get into and in the off-chance that you are unable to get into, there are also other med/health-related degrees that I recommend if nursing isn't your first and foremost passion.
I'd recommend USYD/WSU's Physiotherapy, UTS midwifery (similar to nursing but you have more agency and legal authority for certain procedures), any of USYD Applied sciences (radiography, speech pathology, occupational therapy) etc etc.
If you want more information regarding alternate paths to medicine or any more information regarding nursing, feel free to PM me and I can give you more detailed answers