What fuel cells give you over batteries is a storage mechanism. Batteries are rather incapable of taking large amounts of energy. They're getting better, but the energy density is still far below that of fossil fuels. Which means, you have to have a lot of space and weight in batteries to power a small car. For a larger car, it's even more. Even then, in order to get any kind of range, you have to sacrifice performance. Even the best batteries out there, like Tesla's, don't take a charge very quickly, which sucks if, say, you are in the habit of making 5 hour drives to see grandparents!
Hydrogen may not be more efficient, but it is a more efficient way to store it. You can store large volumes of energy in a small, light package, just like gasoline. Only, you don't gotta burn it and have nasty stuff coming out the tailpipe.
As such, if you want cleaner methods to translate beyond economy cars doing local jaunts between "fill ups", to family sized cars, trucks, vans, etc. that can have decent range and refuel quickly when needed, then you either gotta wait a long time till battery tech gets there, or you gotta look at something like fuel cells.
As for whether it's better than gasoline? For both electric and hydrogen, the answer is yes, albeit it's not nearly as clean as proponents would like you to believe. Electricity has to be generated, so it's only as clean as it's fuel, which is generally dirtier than gasoline. The advantages for electric lie in the fact that, on the consumption end, the internal combustion engine is not very efficient, it makes too much heat. An electric vehicle is very efficient.
Hydrogen is most typically taken from fossil fuels like oil and natural gas, though it can be generated from water using electricity (as the commercial shows, but that electricity has to be generated like the above).
Ultimately I think the near future of autos is still electric and gas/electric hybrids. I thought the Chevy Volt was a brilliant drive system, though the car itself kinda sucks. Far future? Who knows?
But where fuel cells will come into play is in making a jump to renewable sources for power grid applications. Things like wind and solar are too fleeting to base a permanent grid off of. It takes hours to start up a coal or gas turbine and get it running to efficiency, but then it's pretty much steady state. But solar and wind sources wane and surge on the order of seconds as gusts come and die, and clouds cover the sun and then let it out again. Way too fast to start and shut down fossil sources on demand. It just becomes nearly impossible to incorporate a large % of wind and solar into a grid without inducing brown outs and surges.
But if you just take them TOTALLY offline, and let them make hydrogen from water at their own pace, well, then you have a storage mechanism and a medium which can be collected and transported. You can have centralized power plants with a large banks of fuel cells instead of coal or gas powered turbines. And that energy is pure wind and solar energy that's been stored and can now be controlled easily.
As a side note, the latest nuclear reactor designs (which haven't been built) produce large volumes of hydrogen as a byproduct. Likewise, even beyond that, since nuclear fuel is virtually free it costs no more to run a nuclear plant at 100% capacity 24/7. So when grid demand is low you might as well run it and use that extra energy to make more hydrogen as well. So advancing nuclear would go far towards advancing a hydrogen economy.