Microsoft's claim that it's winning the battle against BlackBerry for third place in the smartphone race has been backed up by the release of BB10 shipment figures.Speaking in a conference call after the Canadian giant published its quarterly financials, BlackBerry CEO Thorsten Heins revealed that, of the 6.8 million smartphones the firm shipped in its June quarter, just 40 percent where BB10 devices.That's equal to around 2.7 million units in total, with Heins noting that "there is a lot of work to do" if the platform is to secure a solid footing in the smartphone market.Indeed, it doesn't take a mathematician to note that 2.7 million units shipped in one quarter is - while not a disaster - not especially impressive either.To put BB10's shipment rate in some context, its somewhat down on the 37 million iPhones Apple sold during its latest recorded quarter, and the estimated 70.7 million smartphones IDC believes Samsung shipped during the same period.The fairer comparison, however, is with Nokia, which shipped 5.6 million Lumia devices during its last recorded quarter  a figure that, though a rise over the previous quarter, was nonetheless jeered by some analysts for being too little too late.Nevertheless, given that (according to Adduplex ) Nokia makes up 80 percent of the Windows Phone ecosystem, it's possible to estimate that quarterly Windows Phone shipments are at around the 7 million mark.That means Microsoft's smartphone platform is currently outshipping BlackBerry 10 by almost three to one.Shipments, of course, don't necessarily equate to sales, and neither platform's shipment figures are anything to shout about, but early assessments suggest it's Windows Phone that currently looks the most likely of the two operating systems to secure that much heralded third spot.