Thick or thin?
P3 heads are thicker (P2='grossa'; P3='supergrossa') than P2 heads, which is why they sound more saturated, they have less overtones and transmit an almost matt tone because they vibrate less than a thin head. The thickness of a head has only little influence in how long it may last. A thicker head might last a few gigs longer, but the difference is probably not to be mentioned.

 

Resonance head or batter head?
P3 heads are ideally used as batter heads. You can combine a P3 batter head perfectly with a P2 resonance head.

 

Take some time:
The life career of a head begins with the moment you put it on your drum for the first time. Each time you tune it, the head will fit itself more comfortably onto the rim of shell being the base for the head. Also in terms of sound, time has an effect on every head. New heads often sound a bit whiny when freshly fitted onto the drum. But after a short break-in time and regular playing, the sound will quickly improve. A new head also will lift the rim higher. Each time you tune your drum, the head will sit itself lower down on the base and the rim can settle.
In short:
New head - high rim, whiny sound.
After a break-in time - low rim, nice sound.