The physical world, as an explanation, clearly has more prior probability than the physical world plus fundamental consciousness. (And that seems like a more realistic form of the question. I have yet to see anyone, even those who like to link modern physics with consciousness, actually replace part of the first theory with a new assumption about fundamental consciousness.)
Posterior probability (meaning the amount of belief you should give to each theory after you look at all the evidence, r_claypool) seems trickier. Dualist philosophers might argue that when we fail to logically derive consciousness from the assumption of a physical world, that counts as evidence for dualism. But as gjm suggests, mainstream dualism doesn't seem to change our expectations about certain matters. In particular, it does not tell us when or in what situations a physical process leads to conscious experience. You'd have to describe those situations in ways a physicalist like me could agree with, and add that to our scientific picture of the world along with whatever assumptions dualism entails. On the face of it we can drop the last part and have a simpler theory.
My rant on taking the description of when consciousness happens as an additional law of reality got too long. Suffice it to say, that also seems wrong to me epistemologically.
Background
I was raised in the Churches of Christ and my family is all very serious about Christianity. About 3 years ago, I started to ask some hard questions, and the answers from other Christians were very unsatisfying. I used to believe that the Bible was, you know, inspired by a loving God, but its endorsement of genocide, the abuse of slaves, and the mistreatment of women and children really started to bother me.
I set out to study these issues as much as I could. I stayed up past midnight for weeks reading what Christians have to say, and this process triggered a real crisis of faith. What started out as a search for answers on Biblical genocide led me to places like commonsenseatheism.com. I learned that the Bible has serious credibility problems on lots of issues that no one ever told me about. Wow.
My Question
Now I'm pretty sure that the God of the Bible is man-made and Jesus of Nazareth was probably a failed prophet, but I don't have good reasons to reject the supernatural all together. I'm working through the sequences, but this process is slow. I will probably struggle with this question for months, maybe longer.
Excluding the Supernatural was interesting, but it left me wanting a more thorough explanation. Where do you think I should go from here? Should I just continue reading the sequences, and re-read them until the ideas gel? I'm coming from 30 years of Sunday School level thinking. It's not like I grew up with words like "epistemology" and "epiphenomenalism". If there is no supernatural, and I can be confident about that, I will need to re-evaluate a lot of things. My worldview is up for grabs.