You want both. In fact you want a whole range of different sizes at different locations.

When you design electronics circuits, you place capacitors that smooth the power supply. They’re called “decoupling capacitors” and charge up when the power draw is low, then supply power when the draw is high. The best distribution is lots of small capacitors distributed around, then larger ones distributed less frequently, and bigger ones less frequently again, until you end up with a couple of big ones next to the power supply.

Batteries will become the decoupling capacitors of our national grids.