If you've got $80,000-plus to spend on a car, it frankly seems like a no-brainer to get the 100D instead of the 90D in either the Model S or X, as both cost just $3,000 more. The larger battery in the Model X gives it an extra 38 miles of range, while the Model S gains 41.
Mechanically, the main difference between the P100D and 100D is the drivetrain, as Tesla forum users point out. The P100D option features a larger rear "high performance motor," giving it more oomph but slightly less efficiency (you can see that by clicking between "dual motor" and "P100D" on this product page). As Musk points out in the performance launch post, the P-model battery is also upgraded to safely increase battery output.
To put things in perspective, the Model S 100D still hits 155 mph and gets from 0-60 mph in 4.2 seconds. Sure, that's slower than the P100D's 2.39 seconds with the new Ludicrous Plus mode, but it's still about the same as a Corvette Stingray. Yet, the 20 miles of extra range could easily make the difference between being comfy at home and stuck on a freeway. And the P100D costs nearly $40,000 more than the 100D, which seems like ludicrous amount (sorry) for a bit more acceleration.