I would say the difference between science and religion is religion teaches how to be good, which is subjective, and science, at least the physical sciences, teach things that just are. Being good and teaching broad concepts is different from a tangible, observable science. Also, there are many different religions and there are also many different sciences. "An economist and a political science teacher go into a bar..." You just know they're going to have a field day arguing about what is "best" for us. Science can't even make up its mind regarding true reality yet, with different theories regarding the eventual state of our universe and conflicting theories that arise from superstring theory. Religion is no better, obviously.
It's funny, religion and science got along for a long time. The Catholic church has built many hospitals and schools, for instance. And I think while most people in the United States are Christian, a majority of those people probably believe in evolution too, even to the point of a common ancestor. Religion and science can work together but the problem is the two largest religions haven't been able to keep up with social and scientific advancements in the past 500 years or so.
Look at Unitarian Universalism. That religion is about embracing and accepting people of many different faiths, with a common goal of human unity. UUs don't worship God. They worship fuzzy secular concepts such as *love*. They take their inspiration from any source, ancient or modern. They have life lessons for us all. UUism fully embraces science. They are against climate change and are pro-environmental policies. They are also skeptics. Modern Unitarianism came around in the 1960's, and membership has been dwindling. Its probably because of Christianity's own liberalisation, and the fact that there is no strong reinforcement to go back to the church. The first church I went to was a Unitarian Universalist church.
Uh, sorry. I like talking about myself. What was I on about? Oh, religion and science. They answer two different questions: religion answers why should something be here, and science answers how it got here to begin with. Two completely different questions, two viewpoints. To me, how is a definite answer, whereas why isn't. Why I'm I here? Because my parents ****ed and my mom raised me while I was growing up. Wait ... that's HOW I was here. The question of why is a lot deeper. I answer the question within my own religion by saying this: humans, and all other things, want to live as long as possible with the most amount of options as possible. The longer you live, until you get too old to live life fully you have more and more options available to you. Prolonging death as far as possible and allow one to experience all the options of life is a fruitful way to live, one that should be worth exploring. Along the way you'll see conditions are improving for the vast majority of people. Our natural extropy is accelerating, and one day will reach truly divine place where the big five divinities are not just considered but chosen by a future species. Our cause to divinity is the reason why I live. But that is not the only reason one could live.