I think you misinterprete the conflict between science and religion when you consider it indicating they both understand there is a symbiosis deep down. You seem to think they each think they need the ideas of the other.
I think science fights religion because religion is still largely in control of our modern society and because science has lost the fight in previous individual cases throughout history.
I think religion fights science because religion wants to maintain its control of society, but recognizes the power of science.
I don't think science needs religion, nor does religion need science. Religion could function fine in a pre-industrial, even a pre-agricultural society. Science doesn't need religion, but individual scientists might.
People need morals like what religion provides. Some people need the emotional comfort religious ideas give them. Modern people need science because it's the key to our continued progress and survival. Religion is not a key to continued survival. Religion has been more of an impediment to progress than a help. Religion was especially important early in civilization because it unified clans together to form kingdoms and empires and was often the repository of what science there was. However, religion is no longer needed for those things.
Now, about predictions.
A good theory should make testable predictions. If religion can do this reliably, then it's worth something. If it can't, what use is it? For example, if I do A, B will happen to me. Can religion reliably predict how often religious result B will occur if religious action A occurs? I don't think so.
In the LDS church, they say "If you pay an full tithing you'll never go without the necessities. God will help you out." Then they set up a welfare program so that Bishops will provide the necessities to faithful tithepayers who need it. God doesn't seem to be needed to fulfill the promise.
On the other hand, what about tithe payers in wards without adequate welfare programs? They must go without, but then probably change what they define as "necessities". If they happen to die of starvation then they're not around to complain that they went without necessities.
I think science is much superior to religion. Religion teaches superstitious, non-scientific notions. How can that be equal to the power of science? Religion was made to appear superior to earthly wisdom (science) by inventing miracles for the faithful to perform. However, these miracles were only fiction.
In the LDS church the members are taught that the Priesthood gives men more power than anyone else on the Earth. As a priesthood holder in the church you're supposed to have more power than the President of the U.S.
By religion, I mean a code of ethics, a worldview, and a set of practices based on an affirmative (yes) belief in God. By this definition atheism and science are not religions.
I understand that for someone to be a "religious person" commonly means they attend to church duties faithfully (family prayer, scripture reading, and such things but not necessarily church attendance). You may not do those things yet believe in God. Perhaps I shouldn't call you religious, just theistic.