The big fit difference between Budapester/3636 and P2 is the instep. P2 is lower and more elegant, as well as longer and a bit less supportive. If that fits you, great. I have suede Budapesters in the P2 that are just starting to stretch into comfort for me. On the other hand, I get great support and effortless fit with the Budapester last as well as 3636; those two are nearly the same except for the shape of the toe.
IMO there are significant differences b/w the two last other than the toe.As earlier mentioned Budapester is a shorter narrower last as well as a more tight fitting heel. The ball area of the foot is also significantly snug than same size 3636 lasted shoe.
So in essence if you have a wider foot going 1/2 size up will be a intelligent move.
P2 should not be compared to either of the above but more to the F last. The vamp and toe are much narrower with a lower instep than the F.