Based on our experience, at least the common Avid mechanical “road” disc brakes (BB7 “road” model) have much less stopping power than a good rim brake. We have tested a number of bikes with different rotors and pads, even had a local expert fiddle with one of the test bikes, but there was little difference. The brakes feel great at first, but as you pull harder on the levers, you only get flex in the brake mechanism, but no more braking power.
Bill Davidson has a nice little demonstration. He takes a bike with those brakes, pulls the lever for the front brake to the bars, and then pushes the bike across the shop floor. The wheel continues to turn. He then takes a bike with a rim brake, and the wheel won’t turn.
So I went to my bike, pulled on the front brake lever, pushed the bike, and voila! the front wheel didn't turn. It sounds like Mr Davidson's demonstration is with BB7's, but perhaps from the wording "these brakes" the blogger just means generic disc brakes. I didn't have to pull all that hard. Either way, I'm wondering am I or they missing something?
I don't have any experience with good rim brakes except for the cantilevers on my good cross bike, so I can't compare the two types of brakes much. But my experience is that the BB7's have more than adequate stopping power. I especially like being able to grasp the brake levers easily from the hoods without applying too much force in order to stop quickly. And I hate fiddling with and adjusting rim brakes, so I prefer the disc brakes.
The main thrust of this article was that their experiments found that "on dry pavement, the front brake alone halts the bike over the shortest distance." It's a little hard to tell just how scientific their tests are. Their is an interesting exchange in the comments section between Robert Hurst, the author of The Art of Cycling (formerly the Art of Urban Cycling) and Mr Heine where Hurst challenges the findings and says his experiments have found the shortest stopping distance was with both brakes. I think everybody does agree that you get the most stopping force from the front brake.
(Hurst's website is The Industrialized Cyclist and he has tons of info on his Bicycle Research page.)