The PWM resolution depends on the pin you select for analogWrite(). See analogWrite() in
hardware/arduino/sam/cores/arduino/wiring_analog.c
It does analog out using either hardware DAC, PWM, or Timer/Counter pins else does high/low on digital pins
timer pins: 2-5, 10-13, 58,60,61
PWM pins: 6-9
mapResolution() limits timer and PWM pins to 8 bit resolution, DAC 12-bit.
pin attributes are set in hardware/arduino/sam/variants/arduino_due_x/variant.cpp
variant.h has
#define DACC_RESOLUTION 12
#define PWM_RESOLUTION 8
#define TC_RESOLUTION 8
The chip supports 16-bit PWM on many pins, but the DUE seems to "recognize" only PWM pins 6-9