Opening up the future
As these open source AJAX packages evolve, I think we'll see more of a difference between the ones that are directly tied to one corporation and the ones that remain outside the control of one particular company.
I expect that Google, Microsoft, and Yahoo will continue to exert tighter control and editorial guidance over their AJAX projects, compared with the neutral packages. This control will help people who like a bit more polish and better documentation, because I expect that the vendors will include the efforts of regular staffers.
Such generosity always comes with a price, although it may be small. Yahoo's JavaScript libraries, for instance, will always be there to support Yahoo's mapping business. Dojo's libraries, on the other hand, can work with either Google Maps or Yahoo Maps.
The neutral packages, meanwhile, are bound to grow more varied as they attract more contributions. Some parts of Dojo are already ports from smaller open source efforts that were rewritten to use the core parts of the Dojo packages. I expect that more people will work to add their few lines of code to these projects, if only because it will make it easier for them to leverage the libraries with their own projects. The neutral packages will likely continue to be the ones that offer the most creative ideas and the cutest widgets at the quickest rates.
This schism, however, is just a prediction. Dojo is now supervised by a foundation with support from major corporations (http://dojotoolkit.org/foundation/); perhaps it will start focusing its effort and polishing its documentation. And there is no reason why the bigger companies can't start nurturing and soliciting more contributions to their packages.
Regardless of how they evolve, the best way to use all of these open source packages is to pick and choose the parts you need to assemble the Web application you want. For example, I eliminated Dojo's editor from one of my projects when its text editor didn't offer access to the data in the format that made my life easiest -- so I switched.
It's difficult to suggest one particular library as best or to make blanket statements about superiority because so much of the toolkits' usefulness depends on your programming style and needs. I recommend taking a tour of each and even mixing and matching the libraries. After all, there are few practical reasons why you can't use code from Atlas and Dojo on the same page.