Music Files and Compression

What's the difference between AAC, AIFF, and MP3 files?

AAC stands for Advanced Audio Coding, but is also better known as an MPEG4.
AAC was designed to be the successor of the MP3; giving a similar file size, but having an all around better quality of sound. There is still some crackling or the occasional cut-out in quality, but all-in-all, a much better format.
An Mp3 is the standard file compression for audio files. Mp3 works by compressing the music file enough to fit on a low-memory storage system, but also retain a form of quality. Although this quality formatting is sub-par (Hissing in the background, crackling, messed up vocals and melody), it is still the most widely used file formatting for music.

In a comparison of an AAC and Mp3 compression of the Rolling Stones song Paint it Black; the AAC file had slightly better audio at only a couple mega bytes of increased memory usage (AAC- 7.3MB and Mp3- 5.2MB).

Moving on, we have the AIFF file. AIFF stands for Audio Interchange File Format; and it is the best file format of the three listed above. AIFF is non-lossy formatting; which means that the file being compressed will not be dilapidated like it would be for other formatting styles.
That being said, AIFF blows AAC and MP3 formatting out of the water quality-wise.
That also being said, AIFF is a space-hoarder...
An AIFF format of Paint it Black by the Rolling Stones is exponentially larger than a file of the same song that was formatted in either AAC or MP3.
The AIFF file was 38.1MB of space, when the AAC was 7.3MB and the MP3 was 5.2MB.
Even though the quality is insanely good, the storage used is increased exponentially. But even then, in a world where smart devices and music players have 64GB memories, does that really matter? Sure, you wouldn't be able to hold eleven-bagillion songs on your device; but who even owns that much music in the first place? let alone listens to it all if they do.

If I had to trade in my entire CD collection for a media player filled with my music, I would definitely go with the AIFF format. Because not only would the quality be outstanding, but you can always upgrade the memory on your device with bigger SD cards. (unless you have an apple product, but even then, you can move your music to something bigger with the help of iTunes).