"Excellent" Charge Moves in PvP

Solution 1:

'Excellent' Charged Attacks are more powerful

Completing the charge attack mini-game by swiping around hitting all the circles/bubbles, increases the 'power' of the attack. That is to say, an 'Excellent' charged attack will remove more HP from the opposing Pokemon, than if the same Pokemon used the same charged attack but ending up with 'Nice' or 'Great'.

The Pokemon Go Wikia article on Attacks explains it (emphasis mine):

In Trainer Battles, GO Battle League matches and battles against Team GO Rocket members, when Trainer uses the one of Battle Minigames is initiated. The bonus power of the Charged Attack depends on the player's performance in these minigames.