Better one than the other, but the proper answer is somewhere in the middle. The harder you lock down, the less covid will overrun the healthcare system. Treatment is available, fewer people die even if the same amount get sick eventually, and you avoid system collapse. But also, the harder you lockdown, the more negative consequences lockdown has AND the slower the virus spreads, so the longer you have to remain in lockdown, AND problems exacerbated by turning off people's lives cause exponentially more damage as you lengthen the quarantine.
Imagine a graph where the x-axis is the severity of the lockdown, and the y-axis is damage being done, and you've got two curves to represent the virus and the lockdown. On the left side, where you do nothing, the healthcare system falls apart and the covid damage is way up, lockdown effect is zero. As you impose restrictions to mitigate the spread, moving right on the graph, covids damage plummets while the effect of quarantine only slowly increases, perhaps imperceptibly given the scale of the two. But once you've passed the point where the healthcare system is no longer overloaded by covid, the precipitous drop flattens out, each new measure saves fewer people than the last. But as those measures are added, the negative consequences of those measures compound, AND the duration they need to be in effect lengthens, and suddenly the impact of the shutdown reveals itself as an exponential problem.
I don't think overall it's been an overreaction. My state did some things I think were stupid, shutting down road work for a month is possibly zero gain for a significant loss. But the places that were hit dramatically by covid-19 obviously didn't overreact. The problem is places that locked down disproportionate to their own problems. If a rural state locks down like New York City, they won't get through any of the curve. They'd statistically be looking at months before they find peak infections, and they likely wouldn't have ever overloaded hospitals without any restrictions beyond the most basic social distancing. At this point, the option of genuinely least harm is to relax the restrictions knowing there will be an uptick, because the consequences of staying at home are becoming increasingly visible, and the time they'd need to keep measures in place to avoid that spike forever is still months and months long.