"Public transport" is used mainly in British English while "public transportation" is the usual term in American English. Staszek is of course right that both are correct, but don't see how "public transport" can be much more common worldwide. Even adding together all the British English speakers in the world (including the UK, Ireland, Australia and NZ), this still comes to fewer people than the population of the USA. I'm fairly sure that there are more people worldwide who'd say "public transportation". Not that this matters, of course. Either term would be understood wherever you are.

In Australia, we would say public transport. Eg. "You could get to the airport by public transport" or "Public transport is surprisingly expensive"

Both are correct but "public transport" is much more common.