you can download comparison images the same way you download any other image (using the download button in the tools on the right side of your screen).
The image will be downloaded as displayed on the map so you need to “prepare” it before downloading using the sliders in the left-hand sidebar. Currently image download in the compare mode supports basic download (for more info I recommend to take a look at our user guide or our EO Browser webinar.
Downloading an interactive image is currently not supported within EOB (and I am actually not sure if it’s at all possible). What you can do however is adding the images you want to compare to the pins and create a pin story which you can download as gif.