So, after looking around trying to find more info, it seems that the most accurate measurement for comparison is the combined torque the cars can produce. Doesn't fully answer why, but if you look at the torque and the weight of the cars, the 0-60 speeds fall into place. All of these cars are limited by their batteries as there is not enough power to drive both motors to their maximum, which points out how Tesla dynamically manages power in these cars.
Model 3 AWD - 376 lb-ft (4.4 sec)
Model 3 P - 471 ib-ft (3.2 sec)
Model S LR - 487 lb-ft (3.6 sec)
Model S P - 687 lb-ft (2.2 sec)
A short section of
JB Straubel's blog post on dual motors, batteries and inverters from 2015 which explains why it is useful that the motor power exceeds the battery power:
With the shaft horsepower coming out of the motors the situation is not always as simple as front + rear. As we have pushed the combined motor horsepower higher and higher, the amount of times where the battery chemical horsepower is lower than the combined motor horsepower has increased.
Also, the all wheel drive system in the dual-motor cars distributes available electrical horsepower to maximize torque (and power) in response to road grip conditions and weight transfer in the vehicle. For instance, during hard acceleration, weight transfers to the rear of the vehicle. The front motor must reduce torque and power in order to prevent the front wheels from spinning. That power is fed to the rear motor where it can be used immediately. The opposite happens when braking, when the front motor can accept more regenerative braking torque and power.