I have an LCD that can take up to 70mA for its backlight circuit. My thinking was to PWM this through an Arduino output connected to a BC547 transistor.
One method might be to connect Led-A to +5V, Led-K to the collector and emitter to ground (base to Arduino through a reasonable base resistor).
Another possibility might be an emitter follower (Collector to +5V, Led-A to emitter, Led-K to ground, base to Arduino).
My question is - which is the better way? Can I skip the base resistor in the emitter follower setup? Will either be more efficient than the other?
Can I skip the base resistor in the emitter follower setup
No you still need some form of current limiting. 75mA is on the limit of what you can control through a resistor.
As back light diodes are normally in series then you want all the voltage you can get so a common emitter circuit will be better. An emitter follower will lose a Vbe from the supply voltage.
The way I have seen it done and the way I am doing it with my LCD is with a darlington transistor to ground and a 150 ohm resistor to plus 5. A TIP220 is what I use. Vary the resistor depending on your current requirements.