You will get many different opinions on this, but I would say get the American every time. MiMs are very variable in terms of quality, and the pickups are a little on the weak side.
I have an American P and an American Jazz, and they are both flawless, amazing instruments. (Infact, the P is so good, that the Jazz hasn't been out of its case since the P arrived.) The new 2012 P basses have 60s Custom shop pickups, which sound incredible, and are so much better than the MiM pickups.
Also, have a good think to yourself about whether you really need that Jazz, you said that you love the P neck shape, but the Jazz has a very different neck shape.
My advise would be to go with the American P bass, you definitely won't regret it