There are some applications that are not available for Linux, e.g. Trello or Sunrise Calendar. As long as there is a Chrome App available as an alternative, it doesn't matter much.
However, since I upgraded to 16.04, Chrome Apps do behave differently than with 14.04, 14.10, 15.04, 15.10. They have no unique app icon anymore but show the Chromium standard icon instead. And they are not available via Dash search anymore, which they used to be in the releases mentioned before.
How to make Chrome Apps behave like native apps in Ubuntu 16.04 again?