I think the problem is it's one of those things that someone says, and then people say it because they think it sounds right, and then the next thing you know it turns into something that's gospel. But is it fact? I don't know of any side-by-side comparisons that are referenced, or even any at all to look at. The problem is that no one has really done it controlled, you know with clones, same grow media etc. There's tons of anecdotal evidence of people that say they think they yielded more or less from CMH, but I think the reason that all the grow sites say that HPS still gets better yields is for the simple fact that CMH growers are trying to compare the CMH levels at 630 W with HPS at 1000 W and they're simply not equivalent. But in addition to that, I think most places just tend to copy cat that type of information and so unless you see some actual data showing otherwise, I wouldn't believe it. You're definitely not going to yield as much with a 630 W CMH as with a 1000K W HPS, but you will match the yield of a 600 W HPS and have better quality to boot.
The reason just comes down to PAR. I'm sure you're familiar. Lumens mean nothing. PAR is what the plant wants, etc. But what is the best PAR? Well, as far as I'm aware, the McCree curve.
The McCree curve & HPS vs CMH for flowering - Help!
I think HPS still has its place but if your goal is better light quality and energy efficency, CMH is definitely the way to go. As for CMH vs LED, I don't think the answer is quite so clear. I think LEDs are technically able to get better quality light since you simply have more control over the spectrums available, but as far as the price-point, reliability and other factors go, I think CMH is far simpler to get into.
If you want to look around at my journals, my Panama x Malawi was grown with both HPS and CMH. The grow media changed though, so I don't think the yields are comparable, but you can take a look at the bud growth of the CMH vs the HPS.