When I check both com.au and gov.au sites for the usage of analogue and analog, there is a much greater use of the spelling 'analog'. But when I check all .au sites the spelling 'analogue' is slightly ahead. This is quite significant and requires further research.
Normally the words such as dialogue, catalogue would be considered to be the Australian English spelling, and dialog, catalog, would be the American spelling. The Australian spelling is the same as the British spelling. The British spelling is 'analogue' and the American spelling is 'analog'. So it comes as some surprise to me that in Australia 'analog' is a common spelling.
After reviewing the spelling I found the result to be rather interesting. In Australia the spelling analog is often used as an adjective (analog TV, analog computer). The word analog appears frequently in the electronics field.
I decided to use Search Australia (which limits searches to domains ending in .au) and performed various searches using both spelling variations. Usage varies considerably, but analog appears to be mainly used as an adjective with electronics. On the other hand, with 'analogue/analog clock' the main spelling is 'analogue'.
This does make me wonder that since America has heavily influence our electronic purchases, whether or not this has resulted in the American spelling gaining greater acceptance in one area.
At this stage I can't provide a definitive answer as to which is the preferred spelling. For me personally, the preferred spelling would be 'analogue'. My reason is that for most purposes this appears as the preferred spelling except when used as an adjective with electronics. There may be some cases where it would be appropriate to adjust the spelling (such as in electronics) where consistency may be preferable. I'll leave it up to others to decide their preference.