This is a fantastic question. The difference has to do with what these groups consider reliable evidence. Scientists are aware of phenomenon like optical and audio illusions, mass hysteria, mental illness, delusion, and personal bias, so they don't consider a personal experience to be valid evidence in most cases. If the sample size is very large and the experience is trivial, then it might be OK to use a personal experience in a psychological test (i.e., do you feel a shock now, does this look red to you). But for the most part, even if personal experience is used as testimony in a trial, it's not scientifically valid. There are many reasons to doubt an experience by itself as evidence for something. The most obvious is the existence of an imagination, dream states, altered states of consciousness, disassociation, and our split brain which should make us have serious doubts in the reality of any experience not associated with external events. I would ask, as I have of Jen, how do you know that what you think of as an experience of god was actually a god?
How do scientists know that their experience of physical evidence is real? They do the test more than once. They publish their papers so that they are subject to criticism, and everyone can see the evidence. Everyone can follow the train of logic from basic premises to conclusions. Other scientists perform the same experiment. Even if people do trust scientific conclusions based on authority, they shouldn't. The proof that the scientific method is sound is that it produces results. The technology that has come out of such discoveries are obvious everywhere. We know more and more about the universe every day from scientists. What do we learn from theologians? Nothing new, and in fact many older teachings have been shown to be false. Technology is the proof that science works.
Dark matter hasn't been detected yet, it's only an hypothesis. No one should believe that it exists, only that it's existence would explain some observed phenomenon.
If dark matter were detected, we don't have to trust in the experience of a scientist, only the observation of an inanimate instrument which has no personal bias. Science is accessible to everyone, regardless of their personal beliefs, while god is allegedly only accessible to people that hold certain beliefs. It has been shown that one's beliefs can alter one's perceptions. In other words, if you believe in ghosts, you will interpret bumps in the night as proof of ghosts. Science is a process of eliminating such errors.