The best thing hydrogen has going for it is that it’s easy to scale up without needing significant increases in mining and processing various minerals.

If you are willing to increase mining, and want the cheapest solution, and you can ignore or solve geopolitics, the “best” solution is neither hydrogen or batteries, it’s to make a several square meter cross-section HVDC loops around the planet, because nighttime winter is never more than 20 Mm from daytime summer and the losses are low enough that it is still worthwhile.

But: you probably still want hydrogen and batteries for the vehicles, and vehicles use so much power that solving transport almost automatically gives you enough used parts to build the storage capacity for the electricity grid, and that even with batteries (and over-provisioning PV, which is fine because of how cheap it is), there would be enough storage for winter.