None, but it becomes a bigger fraction as transactions become easier to hide. This phenomenon is mentioned in an article by Paul Birch and my nemesis. (Edit: actually, that article doubles as a warning of how governments are likely to respond to the difficulty of monitoring transactions, and it's neither pleasant, nor the kind that brings about revolutionary change.)
The reasons I had for deeming it superior are that:
That's one thing that (i think) most economists do agree on: the first best tax scheme is a land tax scheme - on the value of the land, not the value added (by building houses, apartment buildings, or skyscrapers).
This is politically infeasible and measuring the value added is difficult, so the second best most economists push for (i think) is a sales tax which at least doesn't discourage productive behavior.
The income tax, on the other hand, is just a terrible idea.
Tangential, but a subject of some local interest:
Why Bitcoin will fail by Avery Pennarun. "The sky isn't red." Thesis:
I'm not sure I buy these and am not competent to evaluate his claims on 3., but would like others' critique.
L019: Bitcoin P2P Currency: The Most Dangerous Project We've Ever Seen by Jason Calacanis. A rather more enthusiastic viewpoint of the project:
The actual text contains many more caveats than the eye-catching selection of points above.