In http://www.eetimes.com/news/latest/showArticle.jhtml?article..., the economics and the efficiency of this process are described: "In fact, with our catalyst almost 100 percent of the current used for electrolysis goes into making oxygen and hydrogen." This is definitely more efficient than the existing electrolysis, as the theoretical maximum efficiency of current electrolysis process is about 80%-94% (http://en.wikipedia.org/wiki/Electrolysis).

I'm not sure what you mean by whether it's more efficient than charging and discharging a battery. But the lifespan of a fuel cell is potentially indefinite and it does not require recharge(add in Oxygen and H+ any time and electricity starts to flow). Further, with each battery cycle, the efficiency of a dry cell decreases.

I think this electrolysis process can definitely make a cheaper form of energy storage than, say, batteries. Even though each anode requires small amount of Platinum, but considering the long lifespan of fuel cell storage, this form of energy storage costs much less than traditional batteries in the long run (all the toxic disposal!) And even for the purposes of propulsion, fuel cell discharge is much more efficient than internal combustion engines.