M4A is MP3's successor. This is why Apple/iTunes has adopted it over MP3, and is sometimes referred to as "Apple Lossless". Contrary to some belief, it wasn't invented by apple, but by the "Motion Pictures Experts Group" which comes up with better encoding formats, starting from MPEG1 to MPEG4 (.h264), with the best now being HVAC (h.265).
I've put this to the test many times using different programs to do frequency analysis, phase, etc. comparing both 128kb M4A's to 320 Kbps MP3 - it may not be audible to the human ear unless you have studio quality headphones, but MP3's, even the highest bit rate possible, you loose almost all sound over 15khz and it reduces the low end as well (although because u loose the highs MP3's tend to sound beefier, but just because they are missing the high frequencies.
M4A vs MP3 is like MP4 (h.264) vs HVEC (h.265) for video - its newer, better quality encoding, smaller file sizes, less quality loss.
" M4A vs MP3: Both M4A (MPEG 4 audio) and MP3 (MPEG3 audio) are audio compression formats, managed by the Motion Pictures Experts Group (mpeg). The following will list the detailed M4A vs MP3 comparison in terms of size, quality and compatibility.
Quality: M4A format is known as the Apple lossless Encoder (ALE), which aims to overtake MP3 and set the new standard in audio compression. It is considered better as far as quality goes when comparing M4A to MP3. Generally, it's recommended to save music as 192 kbps M4A audio to get both great sound quality and small file size.
Size: The general consensus of the file size in M4A versus MP3 is that the former sounds better than the latter when encoded at the same bitrate. For example, a 4 minute song encoded at 128kbps AAC (M4A) would be about 3.8MB in size. To have the equivalent audio quality in MP3 format, you'd need the song encoded around 192kbps, which would make the file larger than 3.8MB.