Pros: cheap, mostly reliable.
Cons: if they lose, steal, or allow your package to be stolen... kafka-esque hell ensues.
In my personal experience, Priority Mail is a 95+% reliable shipping method for small, light packages with some very specific exceptions.
Example 1: A Priority package sent from NYC to Los Angeles with Delivery Confirmation was placed by the Postal Employee in the open magazine bin of an apartment building in Mar Vista, CA. This mailbox area is visible from the street/sidewalk of a highly travelled area. The package was stolen. The Postal Service claimed that leaving a box out in the open is a "confirmed delivery".
Example 2: Another East coast to West coast delivery. This time the person who was supposed to receive the package got a call from an FBI agent who was investigating thefts that were occuring at an East coast distribution hub. When the person who shipped the package checked on the problem, all the postal employee could come up with was "was it insured?". Filing a claim resulted in no response... pure runaround, passing-the-buck and non-accountability. Apparently, not insuring a Priority package means A POSTAL EMPLOYEE CAN STEAL A PACKAGE FROM WITHIN THE POSTAL SYSTEM and the consumer has zero recourse.
The lesson is this: If you ship Priority, it's a good idea to buy the insurance option. Know that if the package never arrives at the destination, you have to wait 45 days before you can make a claim. When you make the claim, you must take the time to PERSONALLY HAND THE CLAIM FORM TO A POSTAL EMPLOYEE at the post office of origin. Twiddle your thumbs while waiting for a response. It might never come.