jQuery Migrate is the more common of the two in our index: it runs on 5,376 websites against 45 for Quicklink, and 3 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.
Quicklink is a JS library which aims to be a drop-in solution for sites to prefetch links based on what is in the user's viewport.
3 sites run both jQuery Migrate and Quicklink. That is 7% of the sites using Quicklink, 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.