As mentioned, the advantage to hydro-boost is that there is braking assistance as long as there is pressure in the power steering system. A great advantage to boosted street cars or vehicles with little/no intake manifold vacuum. I'm not sure if there is a reservoir to store pressure in the case the engine dies.
actually some has a electric motor for backup, just in case. Majority of medium dutry trucks w/ hydro-boost, you could hear the backup electric motor come on when you press the brakes while the engine is off.