Ted Yapo uses an inductor to generate the current pulse through the LED. It generates a sawtooth current wave - not optimal to drive the LED but still very efficient according to his simulations. It has two important advantages:

1. Possibility to use lower supply voltage than the forward drop of the diode.
2. Increased electrical efficiency

When using a lithium battery with voltage 3V it should be high enough for any LED. Typical LED is most effective with currents less than its maximum current and it has considerably lower forward voltage than the rated voltage. If stepping up the voltage is still needed a charge pump may be used instead.

Professionally made voltage converters claim efficiency up to 95%. IIRC Ted Yapo claims efficiency of his circuit is about 80%. With supply voltage 3V and forward voltage drop 1.5V when using a red LED efficiency of a circuit not using inductor may be up to 50%; for a green LED with forward voltage 2.2V the efficiency may be 70%. It is not so large difference. In fact I am not sure if the difference will be even noticeable. Anyway total efficiency of the circuit depends much more on the LED chosen than the electrical efficiency of the circuit driving it unless the driving circuit is very poor.

Using an inductor has considerable disadvantages:

1. To keep efficiency high the transistor driving it must be switched off quickly. Quick turn off time means strong base/gate driver - which will be either complicated or power hungry.
2. Time of the pulse will be probably determined by an RC circuit. Due to component tolerances the time of the pulse cannot be determined exactly. When the pulse is used to charge an inductor its inductance tolerance adds another uncertainty to peak LED current and amount of energy delivered.
3. To keep efficiency high you want minimal resistance in the inductor - transistor - LED path. Using some form of current limiting/monitoring resistor is impossible.
4. And finally the worst part: the inductor forces difficult compromises. To minimize switching losses the blinking frequency should be low. With low blinking frequency the amount of energy in one blink must be high enough to keep overall light output. To store enough energy in the inductor large inductance or peek current is needed. Large inductance means large DC resistance of the coil increasing loses or bulky and expensive inductor. Large peek current needs large LED which keeps high efficiency at such current - again bulky and expensive.

On the other hand NOT using an inductor "frees" the difference between battery voltage and LED forward voltage to anything we want - such as using a resistor for current sensing, or run the oscillator from this voltage effectively using all available battery current (not energy!) for the LED.

I think it is obvious which way I consider better!