I have an Iridium, 5055a I think, purchased through a Federal Govt rebate scheme (which stil exists). It has an attached, rotatable antenna, which can be swapped for a magnetic mounted rooftop antenna.
The phone has not let me down, save one time in heavily wooded forest, where we couldn't get a good enough signal to make a call. I've heard folk on the global star network complain about lack of service. As I understand it, Globalstar have only one satellite servicing Aus, as opposed to several satellites for the Iridium network.