Please include the complete ffmpeg console outputs for each ffmpeg command (and wrap them in the code tag for readability). Your first command will most likely complain: [ipod @ 0x19694a0] track 0: could not find tag, codec not currently supported in container
However it will probably work with mp4 as your output container.
Your second command uses the native AAC encoder. It is not a great encoder, especially at lower bitrates, but it shouldn't be terrible at higher bitrates. Can you tell a difference between "file.mp3" and "output.m4a"? If yes, and if you must re-encode to AAC, then I recommend using another encoder, such as "libfdk_aac" or "libfaac" as described in the FFmpeg and AAC Encoding Guide (specifically the VBR examples). However, it is recommended to avoid re-encode from a lossy format to another lossy format if possible.