N-Channel Mosfet or NPN transistor for Low Power PWM Application
Using a BJT here, with a reasonably well defined Vbe around 0.7V, allows another option : use it as a constant current source. The spread of Vgs values on a MOSFET makes a BJT a better choice for a constant current source.
Arrange for the base drive voltage to be around 1.4V, and add a resistor from emitter to GND. As there will be around 0.7V across it, its value (2 ohms 0.5W) controls the LED current (350mA), approximately independent of supply voltage.

For example:







simulate this circuit &ndash; Schematic created using CircuitLab

At 4.2V supply, with 0.7V across the resistor and 2.05V across the LED, theer will be around 1.45V across the transistor ( * 0.35A) = 0.5W dissipation (at 100% duty cycle), so choose an appropriate transistor and heatsinking.