As I see it there are a variety of mainstream and competing methodologies for creating rich web based applications. One is the AJAX Javascript model another is Adobe Actionscript/Flex model which uses the Flash player plugin as the platform. Another is Silverlight similar to Flash but uses Microsoft technologies and C#.
AJAX
Pros:
Uses web standards.
Can be run without plugin support.
Cons:
Browsers can have quirks in terms of support for different browsers. A framework helps with this though.
Different performance characteristics depending on browser. Safari and Chrome seem to have the fastest Javascript support.
Standalone Javacript can be time consuming to write. Best accomplished with a framework.
Flex/Flash/Actionscript
Pros:
Strong built in media support inside flash for working with graphics and video.
A single and consistent deployment platform (Flash player). If your browser and OS supports Flash then it supports your application runtime environment.
Cons:
Flash is a proprietary plugin not supported on all clients (iPhone, and some open source OSes for example).
Dependent on one vendor to improve performance and maintain runtime environment.
Silverlight has similar pros and cons of Flash, but is not as widely supported as Flash player and/or AJAX.
Try googling RIA, Rich Internet Applications and you will find a variety of information about the various technologies available for building interactive web applications.
Other technologies include Java applets, but are not as common.
The larger question is do you want to use standard browser technologies or a proprietary framework/plugin? In the long run using AJAX will give you the most flexibility, probably the largest swath of support including clients that don't support Flash player, in particular the iPhone. But there may be very specific advantages to using a proprietary plugin like Flash or Silverlight, including DRM if you app requires it. But there are subtle trade offs.
As far as frameworks with AJAX go there is a large selection. Some notable ones include
Cappucino Web Framework
SproutCore
Google Web Toolkit
Jquery
Prototype
YUI, Yahoo! User Interface Library
and many others.