SHORT ANSWER: PHOTOSHOP & KEYNOTE.
Like anything else, there are many ways to achieve an animation similar to this, however the fact that you are asking how to do or what software to use indicates to me that your experience/skill level in motion graphics, animation or even video editing w/ photoshop is still being developed; in other words, you're a beginner. (I do not say that as a put down at all, just as qualifier.)
Unless you are pursing a career in animation or motion gfx the Pro Apps you and others mentioned should not be considered. Any of the Pro Apps (AE, Maya, Cinema, even Motion) have learning curves of hundreds of hours.
However there are plenty of shortcuts to achieve something very similar, one of which being Photoshop and Keynote. Photoshop and Keynote will process will take you +/- 1 to 3 hours and will allow you to output an HD Quicktime file.
The next level up in terms of complexity, control and learning curve would be to use Photoshop and Final Cut Pro (or any NLE that allowed you to keyframe).
Following that would be to purchase a template that you could use in Motion (or AE but I wouldn't recommend AE even for a template unless you really intend on committing yourself to a time investment).
Following that would be to actually make the whole thing in Motion.
All of my options can be achieved by a typical computer techy kinda guy who's creative and doesn't mind following some tutorials and applying themselves.