jQuery is the more common of the two in our index: it runs on 23,028 websites against 18 for JsRender, and 18 sites use both. Counts come from real scans, not vendor claims.
jQuery is a JavaScript library which is a free, open-source software designed to simplify HTML DOM tree traversal and manipulation, as well as event handling, CSS animation, and Ajax.
JsRender is the template library. The library is developed and maintained by Microsoft employee Boris Moore and is used in projects such as Outlook.com and Windows Azure.
18 sites run both jQuery and JsRender. That is 100% of the sites using JsRender, the smaller of the two.
Want to know which one a particular site uses? Look it up and see its whole stack, or compare two sites side by side.