I would say the single factor that is most important in catching fish is how the hook equipped object is moving when the fish has the opportunity to eat it.
I intentionally made that answer very non-specific because it can be interpreted many ways. There are many different forms of movement that have been found successful at enticing strikes, but often only one or very few of them will work at any given time. The anglers who can best figure out which will work in a given situation are the most successful. It is also true that having a larger bag of tricks in terms of techniques to move the fly/lure gives the angler more options for success.