Well, I can't say anything about the HAB, because I've never tried one, but I do love the Moby wrap. As far as I can tell, they are very similar to wear and put on, and have pretty much the same options for carrying positions. HAB has a pocket, Moby doesn't. I think HAB is slightly less stretchy than Moby, which makes it better for carrying heavier/older children, whereas the softer, stretchier Moby is more comfortable for infants. There is also the MobyD, which has either a fleece, cotton, or silk panel on the front, which is less stretchy, and therefore more supportive. (slightly more expensive.)
I think if you google moby vs. hug-a-bub, or something similar you will come up with some more thorough comparisons.
Also, I saw some new and used moby wraps on e-bay for around $35-40US, but I don't know what the shipping to Australia would be.
As I said, I love the moby wrap - Emily is very content in there, and it really isn't that difficult to put on/wear. One try and I had it figured out. I also nursed her in there for the first time yesterday, and that worked beautifully!
HTH.