Well accordingly to this article Browser Face-Off: Battery Life Explored from http://www.anandtech.com IE8 compares well against all the major browsers for using as little power as possible on you laptop running Windows.
“If you're not set on using a specific browser, battery life might be enough of a consideration to get you to try something new, but most users will probably be more concerned with features and compatibility. Based on user statistics, however, the most popular browsers are already the best choices for battery life, so change may not even be necessary. If you're one of many already using IE8, despite detractors it looks to be a good balance of features, performance, and battery life.”
The tests where done on Windows Vista Home Premium and I would love to see the results done in Windows 7, to not only see how the two operating systems compare but also how well each browser does on Windows 7.
Click the images to be taken direct to the review pages.
Above is the results when using a AMD processor, IE8 comes top.
Above is the results when using an Intel processor, IE8 comes top.
Lastly is the results of a netbook running Windows XP SP3 and Chrome 2 comes top with IE8 second.