Answer:
Despite competing advertising claims, any battery's performance depends entirely on the way it is used. The "premium" batteries are designed to deliver consistent power for the maximum period, limited by their size, voltage, shelf life, and chemical energy storage system.
Any individual Energizer or Duracell product may outperform the other brand in any given application (e.g. toys, flashlights, medical devices, cameras). The only general criteria is that more expensive batteries tend to provide better service and reliability than less expensive batteries. The experience of the consumer should decide which battery to use, rather than a generalization by brand.