While he didn't go into detail regarding platforms and the like, EA CEO Eric Brown announced at the Baird Technology Conference in San Francisco that Battlefield 3 has sold 8 million units and has shipped 12 million. To put that into context, 5 million of those sold were during the first week of release and 10 million had been shipped.
That's a fairly impressive achievement, unless you're in a rush to compare to other popular series. If nothing else, this proves that alternates to Call of Duty will sell and sell well, even if released within the same window and against other popular titles.
Without any specifics, it's difficult to say how well the game is doing cross-platform; no doubt that information will be released at some point in the future.