Is religion or science important? I think...they are both important. Without religion, we would've never gotten to where we are--little, if no morals, virtues, sense of what's right and wrong, and the like. In my opinion, we'd be in a lot of trouble if we were without those. People running amuck, killing what they wished, doing what they wanted--no sense of order. (Why would the government or police be any different if nothing taught them to be virtuous?)
Think back, far back in the Middle Ages...if there was no religion, people would have no purpose. Their only hope was to live as best they could (which was horribly at most) for a chance at salvation. Then, religion was their life. Religion that stated morality and what was right. The same religion that influences many of us today, consciously or not. What do they have to do with us, you ask? A seedling with weak roots cannot grow into a stable tree, can it?
Don't get me wrong, I love science--knowing why things work the way they do and applying that knowledge. Without science, we'd have no technology and that would be simply horrid, no? Imagine, no way of getting food (tools are a form or technology, more or less), less communication; life would be much more difficult. Diseases would wipe out entire continents, and I wouldn't be able to enjoy the special effects of my favorite movie.

Science has many practical uses for the individual as well as the whole. It makes life more understandable, in a way.
They say...religion is cosmic purpose and science is cosmic order. Both are important in various ways, each with their pros and cons. To ask which is more important is somewhat like asking which is better, apples or oranges. They're two different things with different uses.
Some final words. All of the above is my opinion, my speculation. I'm neither a devoutly religious person nor a grounded scientist, but a bit of both. Everyone will most likely have their own ideas, stemming from their differing backgrounds and personality. I do not intend to force these thoughts onto you, but humbly ask you to consider it all--consider with an open mind. (I didn't elaborate much on science, seeing how many other posts defend it already.) As for the overlapping beliefs, I believe them both. Perhaps they connect somehow, someway. Flame me, if you will--everyone does.