Next.js is the more common of the two in our index: it runs on 5,505 websites against 227 for Yii, and 2 sites use both. Counts come from real scans, not vendor claims.
Next.js is a React framework for developing single page Javascript applications.
Yii is an open-source, object-oriented, component-based MVC PHP web application framework.
2 sites run both Next.js and Yii. That is 1% of the sites using Yii, 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.