FLAC is the audiophile's handshake: CD-perfect sound at roughly half the shelf space. It was born in 2001, Josh Coalson; now kept by the open Xiph.Org Foundation, and its real weak spot is fitting in pockets: lossless is still large: and charming Apple's own apps.
AAC is MP3's better-trained successor: cleaner sound from the same number of bits. Advanced Audio Coding: the default soundtrack of YouTube, iTunes and most MP4 video. That makes it the right destination when what you need is streaming-grade sound at friendly file sizes.