The Australian PMI will be have a larger China trade influence than markit PMI due to the fact obviously that Australia has a greater share of trade with that country.
USA for example has Canada and Mexico as major exporting markets while Australia has China for the majority of our mining exports (and tourism) due to China being a major manufacturer and close by neighbour.
The spat Western countries are having with China atm is causing a negative effect on Chinese trade.
The Australian Industry Group (AIG) Manufacturing index rates the relative level of business conditions in the sector. The data is based on a survey of about 200 manufacturers.
The Service PMI release is published monthly by Markit Economics. The data are based on surveys of over 400 executives in private sector service companies. The surveys cover transport and communication, financial intermediaries, business and personal services, computing & IT, hotels and restaurants.
My opinion, the sample base is too small for accuracy.