Wow, the Phillips Hue is a 15 dollar LED light bulb with a wifi module. It requires a proprietary wifi router (~$40). The free app can control up to 50 of these lamps. I can't wait to hear about the first time someone replaces all of the light bulbs in a friend's house and starts punking him from outside the window.
I agree with Jeff that the Desktop spectrometer can produce very good spectra of a lamp. This will show you which parts of the visible spectrum are brightest. You can easily compare this type of result among lamps. For example one lamp might have 1.5 times more blue light than red light, and another lamp might have equal amounts of red and blue.
You mentioned color range, which could refer to the total spectral range of the light. It might not be possible to capture the entire range of the lamp because the range of sensitivity of the camera might not include the entire range of the lamp.
You are correct that the webcam will try to adjust its exposure to compensate for the brightness of the scene, so comparing two spectra with each other will not tell you much about how bright two light sources were. If your goal is to know which lamp is brighter, you can use any digital camera. Take a single photo of two or more lamps so that the brightest one is not overexposed. Then compare the DNs (0-255) in each color channel (e.g., Photoshop or Fiji). The photo has to be taken with extreme care so all lamps are the exact same distance from the camera. Lamps might have hot spots, so it would be best to use a diffuser or reflector to average the output of each lamp. This is not very quantitative (without an extremely careful procedure), but can tell you the relative brightness of a few lamps.
It is also possible to find software which allows manual control of exposure of the webcam. Then separate spectra can be taken with the same settings (with the lamps exactly placed, etc). Or any digital camera with manual control can be used to take individual photos of different lamps using the exact same settings and setup. These photos can be of the lamps, or of diffused or reflected light from the lamps, or of the diffraction pattern formed by the lamp light passing through a grating.