I'm am not a image processing expert, but my take on the resolution question is that if you double both horizontal and vertical components you end up with an image which can be quarter the size to fill 1 pixel e.g. a satellite picture able to see a 4 square metre table i.e. 2 metre by 2 metre, would then be able to see a 1 square metre table i.e. 1 metre by 1 metre or in other words an improvement in resolution of a factor of 4.
Samsung says the GS5 "snaps photos with twice the resolution of the iPhone." That is correct -- the GS5 features a 16-megapixel camera, while the iPhone 5s has an 8-megapixel camera.
Maybe I am missing something obvious here, but I would think that double the pixel count in a 2D image would result in 1.414 times the resolution. To get a true 'twice the resolution' would include both horizontal and vertical dimensions, requiring four times the pixel count.
I am no image processing expert, so if I'm in error here please throw some enlightenment my way.