Piercing is significantly more common
To find this, I utilized the data collected by someone on Reddit (as of Jan 15 2021). They combed Archive of Nethys with a script, and pulled out monster information into a Google Sheet. I took a copy of that information and did a count of all monsters that had at least one melee attack of that type, and another for ranged attacks. Here are my results:
As you can see, Piercing damage is vastly more common in both melee and ranged attacks.
Limitations of the Data
Total is not
a mutually exclusive total; a creature with a bludgeoning melee attack and a bludgeoning ranged attack will be counted twice for the bludgeoning total. However, I still think the numbers provide a good representation of the reality.
Additionally, this data may change as more monsters are released: such is the way of things. However, I'd expect this trend to hold as a general principal.
This data also does not address in any way the relative strength of these attacks, nor does it address in anyway that several monsters will have multiple types of these attacks. Perhaps all the piercing attacks are not all that good and likely to be used! (Unlikely, considering Jaws attacks are usually piercing, and are often the strongest a creature has).