Good scenario: user browsing your site, internet connection drops, Google Gears can be used to save all the data until the connection is re-established and can be uploaded to the server. The website mostly functions as the user expects it to, with only minimal degradation of functionality.
UPDATE: Google Gear's LocalServer works at a lower level than I thought, so you can actually hit the offline version of a website without actually having to visit the online version first.
Adobe AIR: easily add value to existing web-sites with desktop application + integration.
Good scenario: user is browsing a site that lets him chat with other users. However, he has to restart his browser for some reason (FireFox 2 is being a memory-pig again, or he just installed a cool new add-in). He launches the Adobe AIR application that lets him continue chatting with his friends even as the browser is closed. He can also leave the application open to chat with his friends so he has one less browser window / tab to keep an eye on, get updates to his friend's statuses on his desktop, etc.
Bad scenario: user sees some exciting new features on your chat website, enjoys using them, but they haven't been added to the Adobe AIR application yet, since an Adobe AIR application is an application that requires updates, bug fixes, and new feature integration separate from your website.
That's how I see it, anyway.