Why do some MOSFETs have a resistor in series with the gate, and others have a resistor from gate to ground?
The resistors are used for different purposes. It's often good to have both. 

The parallel resistor is to ensure that the MOSFET turns "off" if the input becomes open circuit or floats. This could be because of a connector or a microcontroller GPIO being tristated (eg. during brown-out reset). 

The series resistor slows the switching of the MOSFET (which reduces the drive current and EMI at the expense of a bit of switching loss on each transistion) and can provide a certain amount of protection for the driving circuit if the MOSFET becomes shorted gate-to-drain. If you are switching a large MOSFET with a high frequency PWM you need to have a much lower value series resistor from the driver, if any, compared to simply switching a relay or on/off control of a motor.

For example, you could use a 1K series resistor and 100K from gate-to-source. That would only reduce the drive voltage by 1%.