I have the feeling that Flash-based ( or Silverlight-based) websites are generally frowned upon, except when you are creating games or multimedia-content rich applications.
The Flash application/plugin is a closed source pot of serious undisclosed security holes that expose private data, allow modification of arbitrary files on your hard disk, etc.
Flash files are enormous for basic content. There are more efficient ways of doing things
Flash is slow. The plugin on my Windows PC can hog 100% of the CPU time to play some shitty websites.
Flash is non-standard. There isn't a supported flash plugin installed everywhere. Linux users can't run it without jumping through package management hoops. Firefox users on Windows don't get it by default (well didn't last I checked).
Flash is annoying; your users don't want to be bombarded by animations and jingles and junk just to get some basic information.
No back/forward functions unless the Flash designer wanted to implement them in
Can't view a single page without waiting for all the content/scripts that make up that "page" to load. That's really quite painful if all your user wants is a slice of text and you force the multimedia down their throat.
Most Flash-only sites are really bad; the designers seem more concerned with using all of the features of the flash engine rather than presenting something that's concise and useful to the user.