You won't get any useful information out of iBiquity, just obfuscating falsehoods.
This is the scoop, I put together on my blog.
Interesting blog. If I may... $0.02 worth.
First note: HD Radio means "Hybrid Digital" not "High Definition". Just to be clear.
The test you attempted has a few flaws in it. First, the audio path from the source at the station to FM tx and the HD tx was not identical. It can't be for several reasons. The nature of audio processing for FM is entirely different from processing for HD. You can't really compare HD to FM without audio going into both systems, and few broadcasters will ever even come close to doing that. FM processing is in the world of the wild and wooly. The devices used for that job have almost 40 years of development behind them, but the goals of FM processing haven't changed much. However, even classical stations that should, in theory, be lightly processed are actually processed quite a bit. No point in the nuty-boltsy details here, but one of the intentional side effects of some processors is bass boost. Another is image enhancement, and of course dynamics control. What makes FM processing fundamentally different from HD processing is the presence of the pre-emphasis curve, and the restricted bandwidth caused by the 19KHz stereo pilot. Pre-emphasis is essentially a 17dB boost at 15KHz that starts just below 1KHz. A complimentary de-emphasis curve is applied in the receiver. The result is flat response, but reduced transmission noise. The difficulty is that modern recordings have lots of high end material that easily overmodulate a transmitter unless specially processed. The 19KH pilot tone must be transmitted without audio surrounding it, so all audio must be low-pass filtered so that very little energy is present above about 17KHz. The filtering process is complex, and now realized digitally.
By comparison, HD has no pre-emphasis, and no 19KHz pilot. Standard FM processing would not be appropriate at all, and that dictates an entirely different audio processor chain. The two will not sound alike. But which one sounds more like the source material? Who can say? I'd hazard that the FM processor will tend to hype certain aspects, which might make the HD process sound lifeless and dull by comparison. None of that defines how HD can sound, though. You've just uncovered a difference in the transmission chain.
All of the above makes me sound like an HD Radio booster. I'm not, in fact more of the opposite. It's a dumb transmission idea, and IMHO, doomed to failure, but not for lack of audio quality. The low bit-rate is inexcusable, and unnecessary, except for the fact that in the USA, HD Radio is placed on top of existing FM stations, diplexed right in. Dumb idea also. If HD radio was on a separate band, bandwidth wouldn't have been a problem, bit rates could have been higher, and we could even have had 5.1 channel radio. Oh well.
I recently had a new AVR on the bench for prepping for a client's installation. I fired up the HD Radio, and programmed identical FM presets. In our area there are more than a dozen HD signals to play with of varying bit rates. In many cases the HD surprised me. The separation was better than FM, it was more gently processed so sounded less energetic and dense, but with more dynamics, and it sounded lower distortion than FM. That's in most cases, there were some bad HD signals too. The classical station in town had a worse HD signal than its FM, for example.
The experience didn't leave me running out to buy an HD radio for my own, but it did put it in a somewhat better light for me than it had before. FM takes a beating in most reception situations, HD survives better. FM processing is aggressive, HD doesn't have to be. But, FM is uncompressed from a digital bit stream standpoint, where HD radio is beat up bad. It's a trade off, neither is perfect, and the preferences are often situational. I wouldn't give up on HD radio totally, but you might want to try both on each station then pick your favorite. Don't assume the HD Radio signature sound is all the bit-rate reduction, it's an entirely different audio chain too.