If you're filming Handcam, then you probably have superview enabled. If so, you you can't use 4:3 - and you should film in 16:9

However, if you're filming external camera, then 4:3 is a better choice.

When you film in 16:9, we take the following sections of your source video:

If you switch to 4:3 mode, then your GoPro records the data from the full sensor.

We can use more pixels when appropriate.

So - Photos use the full aspect ratio, and are in a more natural 4:3 ratio.
And the Insta edit can use the additional height - so it can take a wider section of the video.