I found lots of HTML5 UI frameworks over there, such as:
There is so much in your question, that the answer won't be easy and won't be definite at all. It'll also be very opinionated. Looking at the list of framework you brought, I see very different things that are hardly comparable with each other. I'll try to group them somehow and add more frameworks to the list.
The main question here is not the pros and cons of a particular framework. The main question is: how much do you want? Did you really mean an application like Gmail or Grooveshark? Or did you mean something like Stackoverflow - a dynamic and not at all simple, but still a website. Let's consider all of these options.
jQuery widgets follow its plugin system. This generally means, that they are extremely easy to use. In order to create a button, you write:
Now if you want to disable it, you call a method using following pattern:
And getting or setting values, e.g. on slider or datepicker, looks like this:
$('#mySlider').slider('value'); $('#mySlider').slider('value', 42);
As you see, jQuery-based solutions have no model. All your data is kept in DOM and is obtained via quirky method calls. If you need to dynamicly process your data, e.g. do some complex validations, load something in background, filter or sort, then you see that this will soon get messy. By the way, this is the problem why jQuery UI team has not provided a grid control yet - they can't do it without a model. In jQuery Mobile you get a nice mobile UI by the means of simple markup, but there is no official way to pass data between pages.
Summing this up: if you have a multi-page website, if you POST your forms, then use jQuery UI or a lighter solution like Twitter Bootstrap.
Perhaps, you want to build something more complex, more application-like (a single-page application?). You know you will need to work with data on client side. What are your options then?
So Kendo and Wijmo belong to the group of frameworks that provide both widgets/controls and some backing model. There are other frameworks like these, that are not jQuery-based, e.g. Dojo Toolkit. Add some dynamic data loading and you'll get a somewhat complex web application. What more can you wish?
Actually, the most important thing is forgotten - how do you structure (organize) you application? If you try to build a single-page app that communicates with server in RESTful way, then you will soon get into a mess if your application has no architecture. The features that are usually required for this are some concern separation (MVC, MVVM), templating, routing and module management. This is where SproutCore and Sencha appear. They provide a comprehensive solution for building web apps, where widgets are just a small part.
But this is not the only way. The power of web is that there are many-many frameworks, libraries, tools out there, smaller and bigger ones, that will help you craft your app the way you like it. For example, consider AngularJS. It doesn't provide a set of controls itself, but combined with Twitter Bootstrap becomes a complete solution for RIA. Or, for example, look at EmberJS, a more lightweight framework from the guy who created the heavyweight SproutCore. It doesn't provide you with a set of widgets either, but is, in my opinion, a very good base for an app.
So here is my final thought instead of conclusion. All those framework usually show you their widget set, nicely looking themes and the other visual stuff. But what really matters is how you will actually develop you application, how you will structure it, where you will implement your logic. Get to know what the framework provides and think through whether you can substitute what's missing.