jQuery Migrate is the more common of the two in our index: it runs on 4,772 websites against 62 for punycode, and 36 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.
A robust Punycode converter that fully complies to RFC 3492 and RFC 5891, and works on nearly all JavaScript platforms.
36 sites run both jQuery Migrate and punycode. That is 58% of the sites using punycode, 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.