core-js is the more common of the two in our index: it runs on 19,225 websites against 3,152 for LazySizes, and 1,648 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.
LazySizes is a JavaScript library used to delay the loading of images (iframes, scripts, etc) until they come into view.
1,648 sites run both core-js and LazySizes. That is 52% of the sites using LazySizes, 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.