jQuery and Ext.js are not really directly comparable. The equivalent to Ext.js in the jQuery world is probably jQuery UI. Which one is better depends on what your requirements are. They are both widely deployed and liked.
I want to say that JSON with jQuery is better or JASON with Extjs is better because I have seen projects with these combination of two so want to know more which combination is good or it is depend on requirement of project.
Which combination of two (JASON + jQuery) or (JASON + Extjs) will have better performance for running application.
The performance of your application is going to depend far more on your own code and understanding than how fast the JS libraries you use are. The performance of both jQuery and Ext.js has been examined by thousands of developers over the years, expect them both to be pretty good.