Not only is a digital crop an absolute loss in resolution, different focal lengths produce different image quality, from the different perceived thickness of the zone of focus at equivalent stop and the stength of the blurring outside the zone of focus.
Edit0: Obviously you're also see the thing you're trying to get a picture of better
Of course ! This can be explained if we have more time. But the basic explanation should never lead us to believe compression is the property of a lens