We are comparing a method of knowledge (science) to a system of belief (faith), which is not known for revising itself based on new evidence. Even when it does, the wrongs are blamed on human interpretation. Science is all about improving ideas to get closer to the truth, and, in some cases, completely throwing out theories that have been proven wrong. Furthermore, the claims of religion are virtually all unfalsifiable, thus cannot be proven wrong. Therefore, comparing religion and science on the basis of falsifiability is a faulty comparison.
Bitcoin isn't a science any more than a Quartz clock is a science. They both apply it, but they are not it. Also, we are not looking at these brands of technologies in and of themselves, but at their dissemination and market value, which very much involves belief, just as it did with preceding forms of money.