In the backstage videos of music videos, you can see that camera operators are filming with small video cameras.
In the backstage scenes of TV shows, you can see that cameramen are filming with large cameras that they carry on their shoulder (or mounted on a tripod).
Comparing the quality of music videos and recordings of various shows posted on YouTube by TV channels, I do not find any difference.
It seems that small video cameras shoot just as well as large video cameras.
What is the difference?
Though you might be watching both productions in 60fps 1080p, TV and film directors and editors work with higher res and/or higher fps in the studio. This allows them more options, if they want to zoom in farther, slow the shot down, etc. Then they’ll just export down to whatever standard format.
Whatever res and fps the small camera has, the big camera can do more.