It is both, or probably even better neither. Elementary particles are not classical particles and they are not classical waves. They are things that behave similar to classical particles in some circumstances and similar to classical waves in others, but they are neither. But as humans have no experience with such things in the macroscopic world, as we lack intuition for them, we desperately want them to be either or the other in order to comprehend them. Ironically this desire is probably what makes them actually more incomprehensible.