Although there is a direct relationship between file size and quality within a given format, it does not necessarily apply across unlike formats.
For example, a FLAC file is going to be twice the size of a 320 kb/s MP3, but you will not hear any difference between them. Technically, the FLAC file is true to the original source and the MP3 is not, but a 320 kb/s MP3 is past the threshold below which which humans can perceive any flaws.
M4A is generally thought to be higher-quality than MP3, but you've got to really split hairs to make a case that anybody can hear the difference. So why doesn't everybody switch to M4A and get smaller files of higher quality? Because outside the bubble of Apple World it's not been widely adopted. MP3 assures the widest compatibility.
Some trivia: M4A is actually AAC in disguise. AAC is how music gets from distributors to your radio station. When you listen to FM radio, you're listening to 256 kb/s AAC-encoded files. AAC retains fidelity better at lower bitrates. 192 kb/s AAC is indistinguishable from 320 kb/s MP3, so 256 kb/s AAC is overkill.