The efficiency is simply the LED forward operating voltage divided by 6V (times 100 for per cent).
The switching circuit, as shown, as no significant effect on efficiency. For greater efficiency you need a switching type current-regulator with an inductor.
Another interesting thing about circuits like this is that if you place a transistor in series with a resistor and switch it at 50 percent duty cycle it makes the resistor look like it is twice as high in value, and that's about all it does. Different duty cycles make the resistor look like different value resistors, but it never increases the efficiency. To get better efficiency the circuit needs at least one energy storage element.