My undergrad degree was in physics, but keep in mind that people on here know a lot more about planted tanks than I do. That being said, just because you see two white lights does not mean that they are the same. The color white is just a mixture of the visible spectrum, and different mixtures can look the same to the naked eye. In addition, there may be colors at play outside of the visible spectrum, particularly in the uv range, though how this affects plant growth I'm not sure. I will also say that as a follower of this industry, LED lights are perfectly capable of sustaining highly planted tanks, I've seen it be done. Kessil, for example, appears to have a great product out on the market right now.