Neither are an energy source. We will power houses with low cost carbon-free energy: nuclear and renewables.
For renewables, interconnection and load and generation diversity will deal with most intermittency issues.
We then provide additional firming capacity with other technology, including energy storage, that in the case of batteries, is probably operating every day, and for pumped hydro and other long duration storage that’s probably operating every week or two, and then some fuel-based generation that’s probably only operating a few days a year.
Hydrogen is probably not a big part of the future power system.