I think this is a difficult question to answer, because in the vast majority of instances I don't think you can place the majority of blame for wars, creation of weapons, or other things that negatively impact humanity's chances of survival on either religion or science.
On one hand, many conflicts and other atrocities that are ultimately justified by religion find themselves far deeper rooted, usually in issues of power, territory control, or desire for riches. The Crusades, enslavement of Africans and Native Americans, Holocaust, and a seemingly infinite number of Middle Eastern conflicts have all been justified by religion, but I have serious trouble believe that any of these would not have taken place if religion did not exist. The desire for power, or money, or hatred for others, will remain constant, and religion often just winds up being the excuse used to rally others to the cause. Without religion, something else would be substituted just as easily.
And as far as science goes, it's tough for me to blame "science" for the creation of weapons of mass destruction. The pursuit of science is simply us trying to learn more about the world and how things will react under various circumstances. If people use that knowledge to create a weapon, and then order the usage of said weapon, I have trouble blaming that on science. It feels like blaming the Chinese alchemists who discovered gunpowder for last year's Las Vegas shooting.
So with all that established, if I had to pick one of the two to be more likely to result in the extinction of humanity under these guidelines, where science or religion actually directly results in our destruction, I guess I'd go with science. I can imagine some sort of Horizon Zero Dawn scenario where we accidentally create killer robots or something while trying to develop useful technology a lot easier than I can...I'm not even sure how practicing religion would destroy humanity. Even religions that have expressly stated commands to destroy nonbelievers seem to have toned that down quite a bit, so I guess an extremely radical one would have to form and then gain access to nuclear weaponry.
