One big difference between the two would be in the tread pattern. While the Pirelli Cinturato P7 has a lug tread pattern with a boxy, compact appearance, the Primacy 3 has directional tread patterns. Thus, it looks taller and sleek.
pirelli cinturato p7
Both the Pirelli Cinturato P7 and the Bridgestone Turanza are great tires. They are both capable of being very reliable in both dry and wet road conditions. Not only that, but both of these tires are capable of absorbing the noise of the road in all conditions so that you are provided with a quiet ride.