There's more diversity in public policy programs. Some can be fairly similar to economics programs (i.e. Harvard, Chicago, and Michigan); some have a quite different focus.
It is generally easier to get into the public policy programs at Harvard, Chicago, and Michigan than their economics programs; likely the same at other schools.
I wouldn't base your decision on the placement of outlier cases. Yes, there are people who have PhDs from public policy programs and got jobs in good/top economics departments. If your goal is to have a job in an economics department, better to get a PhD from an economics department, though there can be some nuanced trade-offs between top PP programs and lower-tier economics programs. No harm in applying to both and making this decision after you see your options.
The main difference is that the required courses and areas of specialization will be somewhat different. If you go to an econ-focused policy school, you'll still take microeconomics and econometrics. You probably wouldn't have to take macroeconomics. In a policy school, you may have the option to take micro and metrics in the economics department or a less-technical version in the policy school.
I think the way to think about this is to start with your substantive areas of interest; i.e. labor, education, health, etc. Then focus your applications on programs (economics and non-economics) that are strong in that.