Maybe a mixture of both? Perhaps the actors can fight cutscene-style in waves. Every time a battle starts, whoever has more AGI will attack first. Say, the player has more AGI. He will then strike first, and then the enemy will strike next. After that, if the player has a certain amount of more AGI than the enemy, he can strike a second time (or vice versa). If both are still alive, the player will then get the choice to either attack again, "swap out" for another actor, or escape.
Healing can probably be done outside of battle (from the menu), or maybe during battle at the cost of the actor's attack. It's a little weird (I think), but I just thought of it on the spot. :V