Importance of Phase in FFT of an image
The amplitude of an image represents the intensity of the different frequencies in the image. Therefore, it holds the geometrical structure of features in the image (i.e. changes in the spatial domain).
The phase on the other hand, represents the locations of these features (which helps our human eye to better comprehend the image).
Here's a visualization I made in Matlab:

As you can see at the bottom, when we combine amplitude and phase from different images and perform inverse FFT, the resulting image looks much more like the original from which we took the phase. This means that phase holds more information about the image than amplitude.