A great live recording/mix makes your live performance video a powerful tool to show your audience what you look and sound like.
Bands/artists should never settle for great video quality synced to poor audio. Current technology makes engineers able to easily capture your performance in multitrack format, so it can be properly mixed in the studio. You should never settle for a 2 track recording from the FOH mixing board, or camera audio for that matter, to be synced with your live performance video. Trust an experienced sound engineer to capture and mix your performance and make it as stunning as your video capture.