Both are JS frameworks and there to help you. YUIs are known to be more natural in them and closer to the original Javascript, while jQuery is known as simpler, and you find more jQuery users and support them with YUI then. However, as mentioned earlier, it depends on the project, if you are likely to create your own widgets, I suggest you go with YUI, but if it looks like a simple e-commerce site in which you just need galleries and a shopping cart go into jQuery, you will quickly learn and implement this. I'm not saying that you can no longer go deeper into jQuery, but my impression is that jQuery is more like CakePHP for PHP, like a framework that quickly pushes you. In my opinion, you do not need to use them side by side in one project, which will simply create overhead, as well as doing what you want to do, i.e. create dialog panels, auto-complete quick searches related to utility events, etc.
I am writing a series of tutorials for beginners and intermediate tiers for YUI users, let me know if you find them useful or if there is anything else where I can help. http://ciitronian.com/blog/tag/yui/
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