What is the difference between doing 1,2,3 or all divine beasts?

Your statement is correct, the only real difference (besides powers), is how the final fight plays out. For each undefeated Divine Beast, you have to face that Ganonspawn as part of a "boss rush" at the end. Each Divine Beast freed will also take away 1/8 of Ganons healthbar during that fight (down to a max of 1/2 if all are freed).

It's also worth mentioning that you get an extra cutscene for each Divine Beast you complete, where the Champion launches the attack from their beast.