AnandTech's Mobile Browsing Battery Life Test Of Recent Smartphones
As always we test across multiple air interfaces (3G, 4G LTE, WiFi), but due to the increased network load we actually find that on a given process technology we see an increase in battery life on faster network connections. The why is quite simple to understand: the faster a page is able to fully render, the quicker all components can drive down to their idle power states.
Funnily, the traditional view is that LTE worsens overall battery performance. However, as AnandTech explain, the raw speed of the LTE results in page rendering completing faster letting the phone power down, offsetting the increased power requirement of the radios, resulting in big net gains.