It depends on the situation and where the package is coming from. Obviously, packs from China and Thailand are going to garner more profiling and inspection than packages coming from say the UK, Germany, etc.
I really don't see a difference between a PO Box and a house address when receiving. To get a PO Box, you have to register a valid house address with the Post Office to get the PO Box. Either way, if something goes wrong (which is the key in this) then they know where to go.
This all depends if you are receiving International or Domestic as well. If you are receiving International, Customs is the one that has the legal right and statutes to open your packages, not the Post Office. If you are receiving Domestic, UPS or FedEx have the right to open your package whenever they wish because they are a 2nd party courier and not protected by US search laws. If you are receiving Domestic, USPS cannot open your package unless they obtain a warrant from a judge to do so.
The difference is this. If something goes wrong (an amp breaking, etc), and a box is leaking, etc because of the anthrax issues, USPS has to notify their police force and agents on every issue in each Post Office. UPS and FedEx do not have those same requirements for their employees and the pressures to look for such biohazard issues are not as prevalent in their companies.
Sorry for the long-winded answer, but I guess it really depends on the situation.