TIP120 is two NPN transistors arranged so that 1 transistor drives the 2nd transistor.http://www.fairchildsemi.com/ds/TI/TIP122.pdf
NPNs need current to turn them on - 1st transistor is used to drive higher current into the 2nd.
Voltage drop across the 2nd transistor collector-emitter is pretty high, 2 to 4V depending on current.
N-channel MOSFET is driven by voltage level instead, needs very little current.
Voltage drop across drain-source is dependent on the Rds of the device and the current flow.
Rds can be very low, like 0.030 ohm, so for 360 LEDs, arranged in 90 parallel strings of 4 LEDs in series, drawing 20mA/string, so 90 * 0.02 = 1.8A,
the voltage drop across the MOSFET would be 1.8A * 0.03ohn = 0.054Vhttp://aosmd.com/res/data_sheets/AOI516.pdf
This might allow strings of 5 LEDs from 12V even, reducing your current draw even more - 360/5 = 72 * 0.02 = 1.44A.
Power dissipated = Current * Voltage
So for TIP120, 1.8A * 2V = 3.6W, gonna need heatsinking.
For a MOSFET, 1.8 * 0.054 = 0.09W, heat sink likely not needed.
MOSFET, want to switch voltage levels quickly, so go from high resistance (off) state to very low resistance (on) state quickly, and not burn up the part going thru the medium resistance region slowly and dissipating more power.