Maybe someone could clarify, but what exactly is being "won?"

I would give a qualified agreement to Hawkings... the scientific method works at expanding our knowledge about the objective world. But science itself does not always work. This interview is proof of that. Doctors used science to predict that Hawkins would be dead 43 years ago. They were wrong. People can use observation and reason and still come to the completely wrong conclusions. This does not make science useless, but Hawkings should have qualified his statement to say science usually works. Or rather, it works more reliably than other methods (revelation for instance) for discovering things about the objective world.

Also, I think the view that all religion is based on authority is a very narrow view of religion and more accurately describes fundamentalists and dogmatism. Furthermore, I'd disagree with him that somehow science is not based on authority. It absolutely is. It has to be. If it wasn't, any crackpot who did a study and got some result that disagreed with scientific consensus would get to have their results accepted immediately.

But there's a huge downside to that--new scientific ideas can take decades before they finally overturn prior "consensus." Adenoidectomies (getting your tonsils out) are one example. Scientific consensus in the early 1900s was that everybody should get their tonsils removed--and nearly everybody did. It took nearly 30 years for researchers to turn the tide and convince doctors that removing the tonsils could actually do more harm than good. Meanwhile, during those 30 years, based on their authority as doctors, surgeons unnecessarily removed the tonsils of millions of kids.

All this is to say simply that science is not some magic bullet. I guess I get a bit annoyed when people try to glorify science. Science isn't perfect, but it's the most reliable method we have for exploring the objective world. That's all you can say about it. And really, that's all that needs to be said.