Is Princess Luna more powerful then Princess Celestia?

Yes, of course she is and I can prove it: Celestia had to use the Elements of harmony to send Luna to banish Luna to the moon, so exactly why did Celestia have a hard time when she was fighting Luna, so Celestia used the Elements of Harmony cause she wasn't powerful enough. So MLP itself proves that Luna is more powerful the Celestia. There I proved it.