I'm impartial but its pretty simple:
pro-monarchy
Can we really be f***ked replacing all the signs of the British Empire? This means starting from scratch and changing the flag, the anthem, the currency, not participating in the commonwealth games (ROFL..) etc etc. It'll take alot of time, effort and cost to do all this. So just leave as is. (scared of change)
pro-republic
The british shafted us long ago and cut all ties in the 1960's to join the EU. It means that virtually all British nfluence has been cut. e.g UK Privy Council used to be highest court of Australia but then they changed it to 'High Court' in Canberra. We used to have to get 'permission' from them before we were allowed to make changes to acts and all that legal stuff. In this day and age, our connections to the "Mother Country" are of a HISTORICAL nature only (the governor general is the only current british entity with any reasonable influence i can think of). We have far closer relations to our neighbours and trading partners (e.g US, japan, china, south korea, asia-pacific etc)
So its kinda pointless still being a member of the commonwealth. All british connections are simply redundant. Once Queen Elizabeth FINALLY dies.....we will become a republic. (realistic and the next progressive step for australia heading into the 21st century).