jQuery Migrate is the more common of the two in our index: it runs on 6,939 websites against 25 for JsObservable, 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.
JsObservable is integrated with JsViews and facilitates observable data manipulations that are immediately reflected in the data-bound templates. 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 JsObservable. That is 20% of the sites using JsObservable, 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.