A recently-posted video shows the Edge browser beating Chrome and Firefox in terms of battery efficiency. It comes as no surprise, though; the test was run by Microsoft, which develops Edge—hardly an impartial observer.
http://www.notebookcheck.net/New-test-shows-Microsoft-Edge-is-kinder-than-other-browsers-to-battery-life.213026.0.html
I can confirm this MS test. Indeed, they're browser is much better optimized when it comes to using resources of the system compared to Chrome (don't use Firefox at all). On a 6700HQ, with GTX950M, if I am running a 4k video on youtube, on Chrome I have 30% or more CPU usage. On the Edge, CPU usage is 1-2% and all the work is the by the GPU, which is more efficient. This is also valid when it comes to memory usage, where Edge comes ahead. I think it is kinda normal because MS is able to do better optimization on hardware resources since they know what is what inside their OS. And in the end, I must admit, Edge is the first browser from MS that is really up to par with competitors and in this battery consumption scenario even better.