Hydrogen, is far better used on more long-haul needs like transport, ferries, air travel, cargo ships, longer distance rail service, and cars. It offers the flexibility of traditional diesel/oil/jet fuel without the emissions and is blissfully quieter. It can used for commuter systems but it has one big drawback............it can never be used on a route with any underground stations due to safety concerns much like diesel can't. As RER ridership soars it may be necessary to build even a small underground alternative station to relieve the stress on Union and with hydrogen that simply wouldn't be an option. Of course it is very promising but also is still a newer technology and will require years to get the kinks out of the system to say nothing of having a number of large fuel suppliers.
Battery trains are very much just standard catenary trains that simply require fewer wires. This gives them the flexibility of running on non-electrified routes, far less initial infrastructure costs, not having to deal with low clearance bridges, and are more reliable due to not being at the whim of Mother Nature. They also have far lower operational costs because they don't require constant replacements, maintenance, and repairs due to weather as wires ones do. The recharging stations can simply be done at each station but are more secure and now require no contact so degradation of the system is nearly non-existent. They also don't have the visual pollution of catenary wires makes them more palatable to the neighbourhoods they are going thru.
Battery trains have been around forever as has the technology and it is proven. The only difference now is that the battery technology has allowed them to be cost efficient and practical.