Like I said, I can't say why without knowing the design of the current limiters in the LED assemblies. Most likely, that working one has a slightly lower voltage drop over the LEDs than the non-working one.
They do PWM because it is much more efficient and easier. The bulbs are 50 watt, so they each take 4.17 amps of current. To reduce them to half power, without PWM, you would need a 1.2 ohm resistor.* That would dissipate (waste) 10.4 watts per light (21 watts total). So, you have to get rid of 21 watts of heat somewhere, and the alternator would need to generate 21 more watts (gas mileage hit). Or, you could do PWM and only waste a watt or two (losses in the switching FETs).
*: Half power = 25 watts, so about 2.95 amps at about 8.47 volts.