Gravitational waves would basically provide us with a model for gravity we can understand thus giving us answers to the only fundamental force we don't quite get. It was also mean gravity is also quantised (providing the waves were caused by the particulate equivalent, the graviton) and with information about the graviton that would lead to a quantum theory of gravity which would be very important. With a quantum theory of gravity in hand we could work towards unifying gravity with the other forces.
So in conclusion both are pretty important as they both help with a Grand Unification Theory, the topmost goal of all of Physics.
Again, I wish I could go into more detail but this is as far as my know how goes. Maybe in 6 years after my shot at University I can help out a little more.