By now, I'm sure a lot of people will agree jQuery is pretty much the standard JavaScript framework (or as much as one can ever be). I mean, it has been adopted by Nokia and Microsoft.
Now that Google has put out it's own framework, is it worth my time learning it? Do you expect good adoption of it because of the Google name?
The library was released on 11/5 - a week ago from today.
This is not enough time for anyone to make a judgment on adoption, ease of use, etc. No one can answer your question because no one knows the answer yet.
Most of Closure consists of a set of tools to make programming Javascript easier. These tools should be compatible with JQuery. Only a small part of Closure competes with JQuery and that is the library. The rest should be useful no matter what library you use.
That said, I think I would wait to see if this gains traction. Google has published a lot of tools and API stories over the years and only a handful gain traction.
The question is, adoption in what context?
If you're building large, custom applications which are Javascript intensive (such as Gmail) and need the performance and speed that Closure seems to offer, then the Closure suite of tools would be a very useful framework.
However, if you're a one-man-band or a small company building lots of simple public websites with the ocassional Ajax call and UI effects (which is most people), then Closure doesn't make as much sense. I think most developers in this context won't see much benefit in using Closure, and will stick with jQuery (or what-have-you) because it will let them get things done quickly.
Different tools for different situations, IMHO.
Sam C is right. My opinion to jQuery is simple: It is very well tested, it is very simply to understand and there are also a lot of plugins out there, that cover most needs. Like a simple but jet migthy Autocomplete.
Let me suggest something out of the box: Try GWT, its made by google, is based on java, supported by IDEs like eclipse and is catching on fast, I made my personal site in GWT and ppl tell me that they didnt believe a sites could be made like that.
of course, if you need it only for basic reasons such as a screen validation or something similar, i would suggest to go for a tried and tested technology..