tons of objective data comparing PS4S and pz4 (not star spec but on the same site you can also find a direct comparison of the standard ps4s vs the star spec) here
https://www.tire-reviews.com/Article...-Tire-Test.htm
The pz4 actually beats the ps4s in wet handling and wet braking. However, they do have poor aquaplane resistance comparatively which maybe is what leads to the perception that they are poor in the rain.