To answer your question, experience and empiricism are very strongly related, but not exactly the same thing. The sciences (whether biological, chemical, physical, psychological, etc.) each rely on the the doctrine of empiricism in their respective philosophies. That is to say, the philosophy of science invokes empirical philosophy as a justification of knowledge.
So the question is, what is the relationship between experience and science? Experience is a label in language for what might be called awareness. In Robert Audi's introduction to epistemology, he cites 5 general sources of knowledge: perception, memory, consciousness, reason, and testimony. What you are calling experience might be understood as a catch-all term for these sources of knowledge. The difference between science and experience, however, is that science is more rigorous and follows some time-tested rules.
Science starts with experience, but then adds philosophical, mathematical, and technical practices. Science requires skepticism, which requires him to doubt his own conclusions. A farmer who sees an entire crop fail might come to the conclusion that supernatural forces are at play, and prays next season and then has a bumper crop. He could conclude that gods were responsible, but science would require him to doubt his own conclusion and find a way to test it. Failures to do so would be experience, but not science.
If that same farmer suspected it might be that a disease were responsible, he might plant two small lots, and rub the leaves of the failed crop on one lot, but keep the other lot isolated and see if there were a difference in results. The farmer might also ask his neighbor about his crop, and compare and contrast the differences in experiences between his neighbor and himself. The farmer could purchase a book on botany and read it to compare his experience to the experience of botanists. The scientific farmer would certainly take detailed notes, make measurements, and attempt to reason through his experience.
So the role of experience in science might best be understood as the collection and reflection on the planting and failure of the crop. If the farmer then chooses science over pure metaphysical speculation or prayer, then he would be attempting to problem solve according to a combination of thinking and experimenting developed over 500 years. This is the role of experience in science.