Note: I've used the Motortrend dyno results as the basis for my data.
Noticed a few topics discussing the merits of the two transmission options. No one has really gone into any technical detail regarding changes in gearing so I'll take a stab at it. The graph below compares the effective torque at the wheels between the 6MT and DCT transmissions. Differences in the ratios are much larger in gears 1-3 than in the higher gears. Shorter overall gearing results in significantly higher wheel torque with the DCT for gears 1 through 3, but this is not the whole story. If you take a look at the areas of the graph highlighted in blue, I've pointed out speeds at which the 6MT results in higher wheel torque. This occurs due to a combination of the DCT car requiring an upshift due to the shorter gearing and the engine torque drop off at higher RPM.
Since no one really uses first gear, I've excluded it from the next plot. Gears 5 and 6 are also omitted since they are effectively the same between the two transmissions. Obviously, gear 7 is gone as well. I think this is a more "real world" comparison. The advantage of the DCT becomes clearer and you can see that there are only a few spots between 20 and 110 mph where the 6MT will be putting down more torque. Specifically, 58-70 mph in second gear and 87-98 mph in third. It's nearly a draw in the 54-58 and 84-87 mph ranges.
I'm not sure this means much in actual day to day driving, but the comparison is interesting. The DCT does weigh more than the 6MT, but faster shifts may offset this disadvantage. With the DCT, BMW has shortened gears 1-4 and added a seventh when compared to the 6MT.
After charting the data, I noticed something interesting. With both transmissions, it makes sense to short shift in gears 3+. This is shown in the following graph.
Optimal shift points appear to be as follows:
