Apollo is a desktop runtime, more similar to WPF than Silverlight (which is a browser plugin).
Sliverlight competes directly with the browser based Flash player.
Flex is an application framework that can target the Flash Player and Apollo.
But Apollo applications can run in either the browser or the desktop environment correct? Or do you have to write/compile your application to both a Flash version and an Apollo version if you want the user to have the choice of either running it in the browser from a web page or run it directly on the desktop?
edit: According to Ryan Stewarts blog entry, Apollo is desktop only. I may be confusing the Trillian "Astra" version with Apollo.