The P3 stores all video and photos on the Phantom's gimbals SD card. However, you can also cache video to the phone/tablet automatically. You can then click these cash'ed videos and they will be moved from a cached folder to a permanent folder. You don't need to be connected to the P3 to do this. These are full size videos. You can also manually download the photos from the P3 but you need to be connected to the P3 at the time to do this.
What I don't like is that there is no option on where these files are stored on the device when downloaded. They are stored on the device's memory only, not the device's SD card (if it has one).