Verses a flash (such as a Canon Speedlite), an LED comes in the handiest in low lighting situations. The darker the better. While that may sound obvious, LED has its limitations, which is why its important to know what your intent is in a particular photo shoot.
For example, I used my Manfrotto Continuous LED Light when shooting my model in natural light. When natural light is not enough, you'll need to rely on an alternative light source to fill in the shadows to adequately illuminate the subject.
In the shot below, the model was too far away for the lights in the LED to be of any consequence. She was perhaps 8 feet from the camera. I simply used auto ISO in this instance instead of a flash. This was not a good instance to use the LED light because of the distance and brightness of the natural light.
However, the LED is perfect for close-ups. In this natural lighting, my model needed just a bit of illumination and since I was 3-4 feet from her, it did the trick perfectly.
I shot some behind-the-scene footage at the Traditional Latin Mass at the Cathedral of St. John the Baptist Catholic Church in Savannah, GA in July. The sacristy of the Cathedral is dim but with some natural lighting... again, the perfect scenario for an LED light.
I highly recommend an LED continuous light such as the Manfrotto for low light situations when a flash and diffuser is overkill. The LED gives the photography the ability to control the light brightness manually and it can be hand held as well. At about $330, it's a pretty good deal.