Yeah, I guess it depends. As Mu naught said, relativity is an example of theory coming before experiment. Black holes are another. They were predicted by theory long before we started seeing astronomical images of them. But in my line of work, experiment often comes before theory. For example, the relativistic high energy jets emitted by active galactic nuclei were not predicted by any theoretical model. They were first detected by gamma ray telescopes, and the theorists are now coming up with models to explain their astrophysical origin.
I guess this is another example of how neither theory nor experiment is more important in physics. Both approaches need each other in order for new discoveries to be made.