For me, I don't have to believe between the two because, firstly, I don't "believe" in Religion, rather I believe in God. Even though I am born (and will die as) Roman Catholic, it's Faith that brings you closer to the Lord. Religion only makes the rules and defines the constraints, yet Faith, or God rather is still much bigger.
But allow me to go back to my point, religion is simply term that defines your orientation (i.e. Christianity, Muslim, Hinduism, et cetera). Believers, or supporters, of a certain religion is also a believer of Science one way or another. They know that there's a Moon, that Earth is a planet, and that the Sun is a star. The only thing that will differ between believers of Science and Religion is that they, believers of religion, will claim that God made these, unlike scientists who'll claim that these came from the Big Bang Theory, or something else.
As for Science, I am currently taking up my pre-med so that automatically constitutes me in the branch of Science. Based from my experience, even doctors cross the line between medicine and faith. They also believe in miracles, but that doesn't imply that they have to stop treating patients using drugs (I'm pertaining about medications here). They still have to rely on the medical procedures and not just faith itself.
You can never place Science and Religion in a single room and hope that the two would come out as best friends. But you can actually make the believers of Science and Religion accredit both without having the need to choose sides because we all see, feel, hear, touch and taste the same things. However, you can never unite them when it comes to origin.
