The iPhone is handling this better because of its automatic HDR.

The LED is white (really, a very, very light pink, to my eye) because it's so bright your camera's sensor overloads and "bleeds" into adjoining green and blue pixels (or because the small percentage of red that gets through the filters on the blue and green elements is still enough to nearly max them out -- another possibility pointed out in comments is that the LED output isn't of high spectral purity -- that is, it looks red but still has some blue and green wavelengths; multiplied by a large overexposure and pixel clipping, this becomes whiter in proportion to the level of overexposure). An iPhone (and many other current smart phones with top-line cameras) automatically takes multiple exposures and combines them to preserve detail across a wider brightness range than the sensor can record in a single image.

If you were to do the same (bracket exposure and perform HDR mixing) you'd get similar results with any controllable camera, regardless of the mechanism making the LED appear whiter than it should.