Google Closure is not the only another JS library, but it is also a set of tools that will allow you to optimize your JS code. Working with jQuery gives you a good set of tools and lightweight functionality, but it does not minify your own code. The Closure compiler will. The closure inspector may also be useful, as sometimes minified code has a different behavior than the original one, and is a pain to debug. It integrates with Firebug and support unit tests, which are both developers' best friends nowadays.
Documentation
Any new library when compared with a well established one, will lack the availability of tons of extensions and tutorial that the established one(like jQuery) has. However, being pushed by Google, it should ensure that support and reliability, both of them will be pretty good. The current documentation and tutorial both seem really good, too.
Features
The features of Closure look decent, though, and its modular architecture is promising too. I guess Google has been using it internally for a long time, which means that you could expect all basic features (and more) to be implemented, and probably in a very optimized and scalable way. They are trying to present it as the STL of JavaScript, so they should have polished it.
After looking at the features more closely, it seems that this may be a step forward for web-applications development compared to existing libraries as jQuery. It guess it benefits internal developments at Google, but things like detecting the online state (see goog.events.OnlineHandler), easy integration of AJAX requests and JS actions in the browser history (see goog.History), or the legions of great widgets they provide (see goog.ui package) may help all of us building even more awesome webapps ;) !
It comes with templates features that integrates with Java (who said GWT ?), so this may also be another plus for Closure.
Ease of use
Finally, it looks pretty simple to use. The syntax may be a bit more verbose than the short $ jQuery function, but with IDEs and auto-completion, it's not a real problem. Moreover, I'd say we can expect a good integration in IDEs like Eclipse, coming from Google.
GWT: Google Web Toolkit is a Java library that allows to create AJAX-enabled web interfaces and that generates (and optimizes) the required JavaScript code. As Google Closure allows to create Templates that can be used both client- and server-side (using JavaScript and Java), my guess is that it will soon be possible to use them jointly (if it's not already the case).
Source: http://stackoverflow.com/questions/1690197/what-does-google-closure-library-offer-over-jquery .