I am in the Uni so I can only type English, if it is OK.
As far as I know in UNSW, most PhD students came here with scholarships. I would say supervisors prefer students who can receive a scholarship. But if the supervisor needs someone to 'work' for him/her, I mean, to supervise a PhD student is vital for their promotion, in this case, he/she would of course love anyone qualified to come.
While being assessed for a PhD offer, the applicant's financial status is normally not considered. So, I would not agree that it is easier for a self-financed student to get the offer. I think it is the same, at least, it is my case. Normally, you get the offer and tuition fee invoice first. You may chose to go and pay the fee. But you may also apply for a scholarship, which is a separate process that follows your offer.
In a word, in terms of getting the PhD offer, your financial status is usually not considered. The supervisor would be happy if you would like to pay the fee after you already get the offer.
Just some of my own opinions. But you will get more chances if you can afford the fee. If you want to become an academic in the future, it is better to get a PhD scholarship. The scholarship is important for you to find an academic job in the Uni.