This processing power equality/competition issue would be mute if in a couple years some super-cooled quantum bits produce something useful. I know quantum computing is years away, but not decades away. In the meantime the existence of bitcoins will act like an X-Prize for revolutionary computing.
When it does happen, it will be like the atomic age: the university team making the first discovery will have to test discovering the next blocks for hours or days against the entire network. It will be a shock, and then the usual volume of mining will resume (if all the bricks aren't discovered first). Like nations in the 1950s, the knowledge of a higher power will be haunting. Then the system will be in limbo until competing quantum computers appear. At least that's how I imagine the processing competition issue to resolve itself.
SHA-256 is not magically broken by quantum computing the way ECDSA might be. A quantum computer which is faster than a classical computer at SHA-256 will be faster than a classical computer at everything, and quantum computers are likely to be marketed to the general public long before the technology reaches that point.