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In the US, 'Professor' seems to refer to several classes of academic rank that are more junior ranks in the Australian system, where Professor denotes a full professor specifically. Are you aware of anyone who tried to assess the signalling benefit of cost of seeking a U.S professorship instead of a local academic position for career capital, authority or grants?
I am not aware of any such cases despite having been working in US and now UK academia for the past 20 years.
"Professor" in this sense tends to be a title of address rather than a job title: US students have learned that in most circumstances it is appropriate to refer to an instructor as Professor (whether assistant professor, associate professor or full professor.... or indeed in many cases even university teaching staff who do not have a PhD yet); in the UK this is only appropriate for full professors, and many still prefer to be addressed by ... (read more)