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.
MP3 is the format that taught music to travel: small, scrappy, and welcome absolutely everywhere. MPEG-1 Audio Layer III. Perceptual coding: it throws away the parts of the signal your ear is least likely to miss. That makes it the right destination when what you need is playing on anything with a speaker, from new phones to twenty-year-old car stereos.