Are you asking about personal energy storage, or grid scale energy storage?
With grid scale, pumped hydro is generally better, as you could potentially take advantage of existing geographical features, or falling that, it's largely a one time investment to dig two lakes at different elevations. The water can easily be obtained from naturally occurring sources, either it was already there or simply wait for rain and runoff to fill it. You can also use the lakes for other things, like recreation, potable water, or even as an ecological restoration project to bring back aquatic biodiversity.
For personal use, hydro gets dicey. Since you're doing it on a small scale, it's very likely that it will be very inefficient, because if you have a reservoir only a couple metres high instead of a hundred or so, you won't be storing much gravitational energy at all. Importantly, you'll have to worry about the tiny amount of energy in your water stream needing to overcome the frictional resistance of your turbine, maybe even friction in your pipes, because you'll be working with much lower pressures and flow rates. Mechanical systems like these are something that generally gets worse in efficiency the smaller scale you get. For example, you might be spending half your energy just overcoming friction with a tiny turbine, whereas only a few percent of a large scale pumped storage system's energy is spent getting things moving, even though the raw numbers of the larger turbine seems worse. Therefore, I'd say batteries would be better for small scale storage in terms of energy efficiency, but perhaps not in terms of longevity or the environmental impact of materials.