Convert MP4 to M4A
Take the AAC audio out of an MP4 and write it into an M4A file, untouched. Nothing is decoded on the way through, so this is the one extraction that costs nothing in quality.
Same codec, different container
Both .mp4 and .m4a are ISO base media containers. AAC audio sits happily in either, and the only real difference is that .m4a tells players and file managers to treat the file as audio. Copying the track across is a rewrite of the wrapper, not of the sound.
That is why the bitrate control is missing from this page. There is no encoder to set a bitrate on. Whatever the video was mastered at, 128 kbps or 256 kbps, is what lands in the M4A.
When to pick MP3 instead
MP3 is worth the second lossy pass in one situation: a destination that will not read AAC. Podcast hosts, older hardware players, and some upload forms still ask for it. Everything else, including every phone and browser in use, plays M4A. If MP3 is required, that page is here.