"Besides price and aerodynamics and maybe weight, are there any other differences in the P2k and P3, like handling, climbing, comfort etc.?"

I can't tell you from personal experience as I have never rode a P3. I asked the same question to the former Cervelo sales manager and he told me that the bikes are fairly similiar but the P3, being slightly more aero, is slightly faster. If you go to the aerodynamics section on the Cervelo site, it claims that the P3 frame is about thirty seconds faster than the P2K frame over 40 kms. Whether the price difference is worth it is something that only you can answer.