jQuery Migrate is the more common of the two in our index: it runs on 5,087 websites against 18 for JsRender, and 5 sites use both. Counts come from real scans, not vendor claims.
Query Migrate is a javascript library that allows you to preserve the compatibility of your jQuery code developed for versions of jQuery older than 1.9.
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.
5 sites run both jQuery Migrate and JsRender. That is 28% 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.