core-js is the more common of the two in our index: it runs on 19,709 websites against 25 for JsObservable, and 13 sites use both. Counts come from real scans, not vendor claims.
core-js is a modular standard library for JavaScript, with polyfills for cutting-edge ECMAScript features.
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.
13 sites run both core-js and JsObservable. That is 52% 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.