Advantage of using an op-amp connected emitter follower for LED driving?
The two circuits do the same things, but with different emphasis.

The opamp circuit allows the LED current to be changed by altering Vref. It also allows the LED current to be completely independent of the voltage drop across the LED. This circuit would tend to be used for testing and characterisation where the flexibility and accuracy is needed.

The switch and resistor circuit does neither of these things, but is simpler, and will usually be adequate once the LED type and desired current has been determined.