jQuery Mobile or responsive design?

Responsive design has little to do with jQM, so you question needs to be modified. - jQM is a widget library that helps creating mobile friendly UIs by enhancing the default UI elements (like text boxes, buttons, and drop down lists, …), handling touch events, and providing widgets (lists, panels, dialogs, …) that covers almost every application needs. It also has some utilities that aid responsive design, like the new responsive tables (introduced in v1.3), and the grid layout (see http://api.jquerymobile.com/grid-layout/). - Responsive design is a methodology that aims at creating websites whose pages adapts to certain traits of the device on which they are displayed on. These traits are for example: Device screen dimensions, device screen resolution, device orientation (portrait or landscape), and many more. At its heart, responsive design depends on CSS media queries to set CSS rules based on conditions related to the traits mentioned above. You may refer to this site for more information: http://bradfrost.github.io/this-is-responsive/index.html

responsive design

Sorry to say - Your question is not much clear so I am unsure that what do you want to ask? Well - Responsive designs is much better and good option to go with. There are alot of tutorials available over the internet which tells how you can make your website design responsive easily. But Bootstrap is BEST responsive framework so far by Twitter team.

Both options are not suitable enough to compare. But still there is a point in your question. You want to develop a mobile site. But whether to use jQuery mobile or responsive. It depends. But one of the advantages in responsive is that, your mobile site can be viewed in desktop as a more detailed website. You don't need to do anything, but the browser will take care of residing the content accordingly (with the use of your responsive css).