It seams interesting to me that what we refer to as the conscious mind is unconscious a third of each day and the part we call unconscious is active 24 by 7.
I'm out of my depth here, but a high-level response:
First, I don't think the "unconscious" part is a single process, but myriad processes, and I'd bet they wax and wane.
Second, the "conscious" part is the part that can reason about itself and think abstractly. I think it would be correct to say it's doing higher level computations. The important part is that this is more costly - it's not optimized because it has to be flexible, so it would make sense that it's resting as often as possible.
So, one high-performance, high-power, general-purpose processor to handle the foreground task, and a bunch of low-power processors for background tasks.
Looks like ARM got it right with its big.LITTLE architecture. :)