They are not orthogonal sets. Science ALSO employs -- esepcially in biology and paleontology -- considerable amounts of hope, faith and belief. Likewise "religion" employs far less of them than you might thing. Both are about organizing things, how best to organize things. Nor need they be competitive.
Scientist, as with all human beings, do hope, have faith, and believe things. They have faith that, for example, what is published in peer-reviewed publications have actually legitimately gone through the peer-reviewed process. The have faith that crackpot IDers haven't surreptitiously taken over the editorship in order to publish crap articles on ID that would not be legitimately published any other way.
Religion, on the other hand, is all about faith, hope and belief . If you are a Christian, you have a book, written by men, that you believe was inspired by God. There is no real proof of this, you just believe it. You believe it because of faith, which is belief that does not rest on logical proof or material evidence. You do it out of a hope for something--eternal life--for which there is no objective proof.
Nor need they be competitive.
Tell that to the Taliban or to the hard-core creationists.