I am on the same track as you, trying to figure out which one will be used for installation on the server side + client side for a huge Internet site. As far as I have seen and read, as always, it depends on the type of web application you need.
There are people using different javascript structures based on simple use, declarative, object-oriented, etc.
Several things can be considered: 1) Client-side technology 1a) “Basic” client technology: frameworks 1b) UI client-side technology improvements 2) Server technology
For the “core” javascript frameworks, you can find JQuery, MooTools (MIT license), ExtJS Core (MIT license) (not ExtJS: these are ExtJS Core + UI gadgets, and later you need a commercial license), Yahoo user interface, etc. . You can compare them on sites like this: http://www.domassistant.com/slickspeed/
This test “somehow” compares various aspects of each of the “core” javascript client frameworks.
What do you get from these frameworks? Most of them allow you to be cross-browser compatible, and each of them has several different ways and syntax.
Just a matter of testing and finding the one you like best.
So with this, you just get the code for "everybrowser".
Now, if you need "Widgets / Controls / UI gadgets", then each "main" structure has its own extension associated with the UI.
Even some of them can interact with each other. I read about an ExtJS implementation (not the core, the one that comes with a few good user interface elements) can connect to jQuery.
So, for the client side, you need to choose your "main" structure, and if you need a user interface, then some user interface is associated with it.
There are several IDEs compatible with these frameworks: Aptana, Eclipse, Netbeans (the latest version integrates very well with javascript) or Microsoft Expression, Visual Studio Express or "Pro".
It is also a fact that jQuery has been enabled "as is" and is supported by Microsoft and Nokia. This way, jQuery will get more attention now, and more support, and more "public", I predict that it will get a lot of attention and improvements. They did not buy jQuery, they stuck to this as an open source, now included in VS solutions. And it will be very closely connected with ASP.NET MVC, components, etc.
In any case, jQuery, as I said, is not the only and not necessarily the best.
It’s good for the server, it depends on your knowledge: java, ASP.NET, which is convenient for you.
I hope you find this helpful.