Hi RVN
The treatment of the 2 pensions is totally different and with your private pension you have a number of options. I have prepared a document which goes through the background and explains the options as well as giving you an idea of the Australian Superannuation system.It also includes a section the way your UK State Pension can be accessed and how it is treated in Australia when you reach the qualification age.
You can download the easy to read document from the following web page
Genesys Wealth Advisers . Just look for the link on the right hand side of the page.
The best advice I can give is get proper advice for your personal circumstances and make sure you are not being ripped off. A decsion made in haste could cost you a lot of money long term.
Hope this helps
Liam