Are there cheaper and more expensive Public Translators?

In the same state, there cannot be. The various state-wide rates are independent from each other, but the rates within the same state are always the same.

Actually you could go checking which is the Brazilian state that has the lowest rates for public translations, and if it has a translator licensed for the language you need. However, would it really be worth the inconvenience, the additional postage expenses and time? And there would still be the risk - according to Murphy's Law - of the rates there being adjusted precisely when your job is on the way. If you are outside Brazil, bear in mind that international courier companies only offer really fast service to some, not all, of our state capitals.

Example: Once a client asked me to make a sworn translation of a document which had been rubber-stamped by a colleague from another state. I told her that she could ask for a reprint from that translator, it would cost half. She replied that it would be a waste of precious time, and asked me to do it all over again.

Word has spread that some Public Translators offer covert discounts, which are forbidden by law. Obviously, the total fee shown on the translation and on the official receipt must match the official rates. Would it be ethically questionable? Definitely! There is no law that prevents anyone from giving away money to anybody they want, so if the sworn translator's client gets some lagniappe in form of cash, there won't be any evidence of it. However one should be wary when hiring vendors with less-than-respectable ethics.