Multimedia Frameworks

Is FFmpeg or Libav preferred for use with mpv?

Generally FFmpeg, simply because it has more features. Don’t expect subtitles to work on Libav. Libav support may be broken at times, because they did not yet add certain FFmpeg API changes which mpv relies on.

Do not confuse Libav with e.g. libavcodec. libavcodec is a library that is provided by both the FFmpeg and Libav projects. Their APIs are almost the same, with subtle differences.