I've noticed some popular browsers out there like opera mini or dolphin mini, but which one doesn't suck life out of your battery fast like the stock android browser?
AFAIK, the "mini" in the browser name means that there's an abbreviated set of things you can do, and it will be designed to work with the mobile versions of the web sites it loads. That in itself shouldn't make much difference in battery life.
A better (even more battery-efficient) browser may suck up more battery life if you use it more, load more web pages, etc. And better to use WiFi than mobile data, I think.
But I think the real problem is that when you surf the web, the device's screen will be on and re-drawing itself frequently. That's what's going to chew up the battery.
So I'd go with the browser you find easiest to use and not worry about how efficient it is.