All in all I see many correct answers here, however, rather than just reference performance inquiries, or just look for features, I have another theory.
A few things to consider (as I did beforeofficially setting jQuery as the Lib I use at work and home):
- Industry standards: Simply put, what is going to be the most versatile among multiple platforms as well as, what looks like it will continue to grow with the industry.
- In my opinion this more important than any other factor as this will help determine both the life of your web-app/sight and the extensability
- It's been my find (through personal research, not gonna list the things I looked at and did as it would get lengthy) that jQuery best meets these qualifications, however, you might look at what you want your sight/app to do and see how those features are used on multiple platforms to best determine if this is the same measure for yourself.
- Almost forget(edited in) SECURITY!!! I didn't see too many people mention this, but something to think about. For instance, Prototype tends to be faster than jQuery, especially in ajax calls, however, this is because jQuery does MUCH more behind the seens to ensure the "security" of you ajax call as well as giving you all the tools you need to set these securities manually, where as Prototype does very little behind the scene work and expects you to use their class system to create your own security measures on ajax calls. This is the definitive number 2 thing to look for in js libs as js hacks are some of the most widely used at this time!
- In my personal opinion, feature richness is just slightly ahead of performance, because, while a lib may lack in performance, what it offers in features will (if it's a good lib) continually be updated to improve its performance. Thus making feature richness more important.
- as a sub-conclusion here, also look at ease of use in these features. One thing I tend to like about jQuery over some of the others is its repetitive use in "styleing" of the code. They are very forcful with how plugins are writtin for their lib thus making everything easily importable and useful in that I dont have to learn new mark up to understand a plugin. This is VERY important to me.
- [Edit-2/14] As another note, don't be too "impressed" with features, as that too can get you in trouble. My example, jQueryUI vs all other UI extension libs for jQuery. Some people jump on those other jQuery UI Libs because they offer more complete, "all-in-one" features, but soon find themselves stuck in a pickle. I like that jQueryUI is limited in its features, as they only include what may be absolutely necessary to start, leaving you to "plugin" anything else you might need.
- Finally, performance, performance is important, however, as mentioned before, many lacking items of performance can be made up for by an easy to use mark up combined with feature-richness combined with proven growth. Alot of recent(3yrs old still, but compares alot of known types) information about performance can be found here.
All in all, these are just my opinions, but some things to consider when deciding on a new change in code. One last thing I didn't mention, how easy will it be to convert your code? If you've already used jQuery for a while, then you've prolly already made so much use of its "easy" features, that, at this point, a code change could set you back weeks or even months. My personal suggestion would be to "go with what you know" but at the same time, to maybe, as a side project, study something else you are interested in until you have a grasp enough on it to make that final decision and possible change.