I'm not sure that these are two competing models.
I remember some online discussion over the merits of FAT vs. NTFS, and then some Apple guy came by and said something like "Apple users don't even know they have a file system". I think this made the Digg front page. The point is that MS and Apple are indeed trying to get away from the file system, especially on mobile. Folders and files are perceived as being too technical and the approach is "Open your image editor and edit your images, you don't need to go turning your computer upside down to look for them among all the other stuff". So the content became very strongly coupled with the app and not so strongly associated with a file type, not as much as it used to be. People are talking about "opening that Word" or "sending that Powerpoint" (maybe in English not so much, but I see it constantly in other languages).
Since most people use a single app for each type of content, the app becomes their "channel" to that content, so it becomes very strongly associated with it.
Also, content-centric means going by files, and we have thousands of files - as opposed to about a dozen frequently-used apps, tops. So it makes a lot of sense to first choose the app and then the file. Which is why apps inevitably get to the front of the work process.