Depends on how much energy you want to store and how long you want to store it.
Not really, no.
The size of a battery is directly proportional to how much energy you store. If the battery provides a megawatt for ten hours, the battery weighs ten times as much as a battery providing a megawatt for one hour. On the other hand, for a fuel cell, only the storage tank is proportional to how much energy you store (and the storage tank is by far the cheapest part of the fuel cell system). The longer the storage period, the more attractive fuel cells are.
If you're rolling it around on wheels, maybe.  For a fixed installation, weight has exactly zero relevance.  You're putting it on top of a concrete slab on top of dirt.  Who cares how much it weighs?
Volumetric density might matter sometimes.  Typical density for hydrogen peaks at about 40 kg per cubic meter (assuming Google search isn't lying to me).  With a fuel cell, this will maybe give you 1320 kWh.  But then you need additional space for the fuel cell itself, plus compressors to compress the hydrogen on the way in.
Batteries give you half the energy density, but that's all you have to have.  Electricity in, electricity out.
Which one is more dense depends entirely on A. how quickly you need to store the incoming hydrogen (size/number of compressors) and B. how quickly you need to be able to turn the hydrogen in your tanks into electricity.  Because the batteries will be instant.  The power is just there.  Whereas with fuel cells you need more/bigger fuel cells depending on how high your kW output needs to be.  So storing huge amounts of power is more dense with hydrogen if you only need to dribble it out, but massively less dense if you need to dump all of the stored energy in an hour or two.
And realistically, for grid-tied energy storage, that second case is more common than the first.  You aren't going to store energy for a year unless you're in Alaska had have all-day twilight for several months.  No, you're going to store the energy during the day and use the vast majority of it between the middle of the afternoon to the early evening.  It's probably a three or four hour window in which you will be dumping all the energy that you stored, give or take.
But to make matters worse for hydrogen, they're talking about burning it, not using it in a fuel cell.  The efficiency there is maybe half the efficiency of a fuel cell.  So when used in that way, batteries are more efficient in terms of volumetric density than hydrogen even BEFORE you factor in all the space for the turbines to burn it and turn it into electricity!  This is absolutely *insanely* space-inefficient.
Add to that the problem of hydrogen embrittlement, where you have to keep replacing those storage tanks every few years, not to mention the pipes, turbines, etc., and it quickly becomes obvious that this project is a giant money pit in which Southern California will burn dollars and turn them into a negligible amount of temporary power storage.
There's no way in this world that burning hydrogen from electrolysis at somewhere in the neighborhood of 20% round-trip efficiency makes sense.  This is quite possibly the single most clueless idea ever to come out of California's government in the history of California's government.  The only people this makes sense for are the ones who are bilking the taxpayers by building out this infrastructure.  Because it will never be useful.  It will always be more efficient to use the incoming energy to charge batteries, or to do something else.  Even when you're talking about things like nuclear power and using waste heat to crack water into hydrogen, you'd still be more efficient with any number of other thermoelectric energy capture systems going straight to electricity and storing it in a battery.
Hydrogen is not the answer.  Hydrogen is the question.  No is the answer.  Always.  For literally any purpose you could possibly come up with other than fusion.