That's not easy to answer. There are a lot of variables that go into that. First, from my research, it seems that quality optics are just as important as the LED's themselves. There are currently two methods, high intensity, high wattage LEDs -or- lower wattage LEDs and high quality lenses. From what I can see, the second approach seems to be the best. So the real question is, do you want to compare a high quality LED fixture VS a high quality MH lamp? If you try and compare a low quality LED, nothing will get proven IMO. Again, I'm no light expert, this is based off the brief research I did when I decided to go LED. LED VS MH was a huge concern for me so I wanted to know a little bit about what I was getting myself in to.
If I could, I would love to see a comparison of an AI fixture over a 10g nano and 250w MH with a quality reflector over an exact 10g nano, both plumbed together with the exact water flow, temp, etc, etc. I think that would be a somewhat accurate comparison though I wouldn't submit it to a scientific journal. It be more of a fun pseudo experiment.