It's really not the same, for a number of reasons.
That's true! The comparison to a nuclear reactor is senseless, but on the hydro dam side: No additional distribution infrastructure is required, in fact the power is available nearer the point of consumption so it actually reduces infrastructure demands. Output can be switched more rapidly than hydro. No water has to be pumped uphill to recharge it. There's no single large infrastructure target attractive to terrorists or other enemies. The owners pay for installation and maintenance, The People don't have to foot the bill. There's no carbon or methane release caused by flooding an area and creating anaerobic decomposition there. Power is available to at least someone even if only local infrastructure is available.
The comparative drawbacks all occur in battery production, but that is only expensive (whether we're talking about economic or environmental costs) once as recycling batteries is cheaper than producing them from scratch, especially since we got technologies that allow us to stop baking electrolyte.