I have a 73 P13 and had a 72 P15 and they were different geometries. Different wheelbases, different curve in the fork. Functionally the biggest difference was the greater tire and fender clearance on the P15. It was set up for 27" wheels with 1-1/4" (32mm) wide tires using Weinmann centerpulls with room for fenders whereas the P13 used 700c wheels using standard reach Campagnolo sidepulls which can still take a decently wide tire by today's standards. The P15 also has eyelets for racks and fenders on front and rear dropouts.

They both ride well. I like the additional functionality of the P15, you can do more things with it.