Here's my comparison of the two:
HaB - Made from 100% cotton jersey (think quality t-shirt material), approx. 6m (6.5 yards) long , approx. 46cm (18") wide tapered ends, edges are finished with a coverstitch (a style of hem), center pocket with drawstring, comes with instructional video. The HaB is manufactured and in Australia by an Australian company.
The main advantages to the HaB are the instructional video (which is really great) and the pocket, which is stylish and can be used as a drawstring bag for storing the rest of the wrap. The fabric is lighter weight and narrower than the Moby, which could be an advantage in the summer.
Moby - Made from 100% cotton knit fabric (think quality t-shirt material), approx. 6m (6.5 yards) long , approx. 60cm (24") wide tapered ends, serged edges, comes with written instructions. The Moby is manufactured in Thailand by an American company. (The owner's father lives in the village where the wraps are made, and they use fair labour practices.)
The main advantages to the Moby are the extra width which enables you to do a back carry (the HaB just isn't wide enough to be secure for back carries in my experience, though I know someone posted on one of the boards recently that they use it this way), and the price.
I personally prefer the Moby Wrap.