MP4 vs MP3: what is the difference?
One carries pictures and sound, the other carries sound alone. That single difference decides everything else about them.
What each format actually is
MP3 is an audio format and nothing else. It was designed in the early 1990s to make music files small enough to move around, and it does that by discarding the parts of a recording that human hearing is least likely to notice.
MP4 is a container rather than a single format. It holds a video track and an audio track side by side, along with things like subtitles and chapter markers, and plays them in sync.
Size, and why it differs so much
A four-minute song as a 192 kbps MP3 is roughly 5.5 MB. The same four minutes as 720p video is somewhere around 30 MB, and at 1080p it can pass 60 MB. The picture is simply far more data than the sound.
If you only ever intend to listen, taking the MP4 means carrying the video around for no reason — and on a phone with limited storage or a metered connection, that adds up quickly.
Which to choose
Choose MP3 for music, podcasts, lectures, interviews, and anything you will play with the screen off. It plays in every music app on every platform and takes a fraction of the space.
Choose MP4 when the picture matters: tutorials, gameplay, anything you plan to edit, and anything you want to watch offline. It is the most widely supported video format there is.