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.
FLAC is the audiophile's handshake: CD-perfect sound at roughly half the shelf space. Free Lossless Audio Codec: think ZIP for sound: it decompresses back to the exact original. That makes it the right destination when what you need is archiving music with zero quality loss and a genuine size saving.