jQuery Migrate is the more common of the two in our index: it runs on 7,001 websites against 1,514 for Select2, and 415 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.
Select2 is a jQuery based replacement for select boxes. It supports searching, remote data sets, and infinite scrolling of results.
415 sites run both jQuery Migrate and Select2. That is 27% of the sites using Select2, 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.