AAC is MP3's better-trained successor: cleaner sound from the same number of bits. It was born in 1997, an MPEG all-star team: Fraunhofer, Dolby, Sony, AT&T and Nokia, and its real weak spot is older or stubborn hardware that only ever learned MP3.
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.