It really depends on how long the power is out. Crossbows were a fearsome weapon of war during the time in history when guns still weren't that accurate or easy

It really depends on how long the power is out. Crossbows were a fearsome weapon of war during the time in history when guns still weren't that accurate or easy to come by. If there's a gap between "people using manufactured ammunition they stockpiled" and "people figure out how to manufacture ammunition and gunpowder reliably like they were in the 1800s before power was ubiquitous", then a crossbow would do quite well.