I find it amusing that they haven't even bothered to change the markings on that particular pcb!
Here's another site that describes some differences in more detail, including the chip markings. If what they state is true, viz, that the Honeywell module is being discontinued and the Chinese one is taking its place, then very soon (if not already) the QMC will be the prevalent one. Most current web sites aren't even aware of it, and specify for the HMC.
As far as I can tell the only differences are a different I2C address and some minor changes in the registers. The APIs can easily be made the same. I am writing an Arduino version that should support both (hope I can still find an HMC to test against) and if that works OK, I'll see you over at the github dev site...