IME the best diet is a high quality pellet (I prefer New Life Spectrum).
Live foods can introduce pathogens. They are also frequently underfed, overcrowded, and living in poor conditions. Unless you raise the live food yourself I wouldn't feed it.
Frozen food has effectively all the nutrition of live food without the risk of pathogens, poor nutrition, etc. Any frozen food is usually just a source of protein, brine shrimp included.
The reason a high quality pellet is best is because it is a complete and balanced diet. It has the protein, fat, and carbs needed and in the proper proportions. It also has a whole lot of supplements that are vital in a complete and balanced diet. Without these the fish will have health problems long term.
The main goal of any diet is complete and balanced nutrition. Classically this has been achieved with variety. But with the right prepared food it is possible to achieve this with one food.