There are arguments for all of these. The two specific options (Dragon or Basilisk) are the ones I will give example(s) for, but you can share theories and such in the comments.
The image shown is the early concept art for the Ahamkara. In the image, we see no wings, but a large snake-like creature.
Now, for the much more popular theory, that the Ahamkara look like dragons. This theory is backed by many as the Ghost Fragment "Warlocks" stats that the Ahamkara are dragons that made promises. Dragons, tend to be depicted as having wings. However, the term "dragon" simply means a monster like a giant reptile. As for more shoddy information, Xur has been quoted saying "There are no birds where I come from. The things that fly, are like shadows". Shadows could mean obscurity, which means rare. And the Ahamkara, would most definitely be rare after being nearly hunted to extinction. Or, I could be crazy, and shadows could actually mean, shadows.
Edit: The flying creatures on Venus are not Ahamkara. They are batadactyls, as said by a [b]Bungie dev[/b].
Edit 2: http://youtu.be/xUfxnDAAxHI
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I can't remember the exact grimoire card, but I know that they have been compared to "overgrown bats" which seems pretty believable. I feel like they look like a bat, except without fur, and with a tail and feathers. They would have scales and feathers just like a dinosaur.