Given a recent question just asked in regards to whether or not Occam's razor supports solipsism, I thought it would be prudent to ask whether the explanatory value of both theories (solipsism vs. the external world being real) are equal.
To make things a bit more interesting, let's assume that under a solipsistic theory, our experience follows certain laws, which happen to be the same laws in physics.
Thus, in order to generate our conscious experience, certain laws and initial conditions are all that is needed to predict the forthcoming parts of our subjective experience.
Now, in order to generate the events of the real world under the theory that the external world is real, the same laws and initial conditions are all that is needed to predict the events of the universe.
Thus, can't one argue that the explanatory power of both theories are actually the same, contrary to the notion that solipsism has inferior explanatory power? If someone retorts and asks "what generates our conscious experience in solipsism? It seems to come from nowhere.", the same can be asked for the theory that the external world is real. As far as we know, we do not actually have an explanation for what generates our conscious experience in the traditional, materialistic view of the world.
So again, is there a difference in explanatory value between solipsism and the theory that the external world is real? Or not?
EDIT:
One thing I can think of from a pro materialist view is that it may make no sense for laws to operate on an immaterial reality. What are the laws acting upon if there is no ontological difference between components of experience?