Bottom line: "e-diff" brakes the wheel with less traction. This has been part of the DTC/DSC system for a long time. The current algorithm does not allow for complete freedom of the DTC system. Hold that button down for as long as you like and you are never completely free (shades of Lexus big brother legal section). The older system allowed complete disabling, so yes, in some conditions you can get more one-wheel spin with the old model. But BMW "e-diff" does not involve any changes to the differential. It never changed. The only changes made were in the software controlling the braking in the DTC system. But "e-brake" wasn't a very catchy label to sell sporty BMWs.
BMW "E-diff" is deceptive lingo, plain and simple. Some marketing peanut in AG no doubt read about the real e-diffs in Ferrari and Porsche and figured they could dupe most of the buyers most of the time. Starting with a crew of 135 fanboys that thought they really had something over the 335s.
Funny how such a wonderful thing has not found its way into the M3 -- thank God!