Thin or thick?
P2 heads are thinner (P2='grossa'; P3='supergrossa') than P3 heads, which is why they sound lighter, they have more overtones and transmit sound easier because they vibrate stronger than a thick head. The thickness of a head has only little influence in how long it may last. Some percussionists play a thin head just as long as a thicker one.

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.