I never played the original, but I can describe how this one plays. You touch to move Neku around during exploration and your partner usually follows unless they're running off for plot reasons. During combat you can tap enemies to make Shiki attack them, or swipe downward to make Joshua attack them, etc -- each partner seems to have a different gesture, and if that gesture matches one of your pin's gestures you'll end up doing both attacks at once, which helps build sync. During the golden bat boss battle the screen would scroll upward to Shiki when you had to uncover the lights.