AFRC guarantees the lowest memory footprint, but bandwidth reduction depends on the image being compressed. AFBC uses variable bit rates which require slightly more memory than uncompressed images, but can compress some blocks (e.g. solid color) better than AFRC.
AFRC supports a subset of the texture formats supported by AFBC. AFRC is lossy, which might not be appropriate for attachments where uncompressed values are needed.
The extension controls the type and level of compression applied to images. Additionally, it may also be used to check if a given image (e.g. the swapchain) is being automatically compressed with AFBC.