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.
WMA is Windows' old house band: big in the early 2000s, mostly retired now. Windows Media Audio, in several variants including a rarely-sighted lossless one. That makes it the right destination when what you need is keeping aging Windows Media software and old archives happy.