At least according to the Center for Sustainable Energy Systems at Fraunhofer USA

Fraunhofer USA Inc. tested Internet Explorer 10, Google Chrome 26 and Mozilla Firefox 21 for their energy consumption on Windows 8. For their study, researchers tested the browsers on desktop and laptop computers in several common scenarios including:

· Browsing the most popular websites in the United States.
· Playing video content through Adobe Flash.
· Playing video content through HTML5 video.

In the above scenarios, Internet Explorer 10 exhibited the lowest energy consumption. In some scenarios such as playing Adobe Flash video on laptop PCs, it was 18% more energy efficient than Google Chrome, and it was 17% more efficient than Mozilla Firefox in playing HTML5 video.

  Internet Explorer 10 is the Most Energy Efficient Browser on Windows 8