MOV is Apple's homebody: gorgeous on a Mac, awkward everywhere else. It was born in 1991, Apple's QuickTime team, and its real weak spot is traveling: Windows, Android and the web would all rather meet an MP4.
OGG is the free spirit of audio: open, patent-free, and quietly brilliant at looping game sound. A container usually carrying Vorbis or Opus audio, both open and royalty-free. That makes it the right destination when what you need is games and open projects that want seamless loops and zero licensing strings.