Well the title seemed simple enough but your actual question has me a bit confused..
I think your asking what web browser hurts your battery the most...? is that right?
If so i will say its not the web browser that matters at all.. Its that giant screen we all love.... Even more so its how bright you set the big screen. Overall web browsing doesn't use much battery life... Some things like playing videos will of course require some extra juice to ask for and receive that constant stream for our enjoyment.... buts its the screen thats the real killer... Set it as low as you can bear to maximize performance..
It's hard to say, but as litlprince2 stated the screen is the biggest battery drain. Also web browsing over WiFi will be different then browsing over LTE, signal strength also makes a difference
The web browser doesn't hammer the battery. The onscreen time and a weak signal will use up the battery. So the more you surf the web, the more battery will be used.