"The bitcoin forum have more libertarian computer hackers than any institution in the world! Let do battle for economic dominance, Greenspan." - Kiba, 2010.
Good thing about this battle is that it will be easy to judge. We'll just have to see which money will survive the other.
Even if it's quite an unfair game, since dollar is basically backed by US army and police force, my bet still goes to bitcoin.
It's true that Bitcoin has no enforcement wing, but the last time that the US Congress inflated the currency that the military was paid with, we can within inches of a military takeover. If it wasn't for Washington, we could have ended up with a military dictator as fast as the French did. It's were the old phrase, "not worth a Continental" came from, and not because the Continental note was worth much. It's really dangerous for the Fed to inflate with abandon, and they know it.