AK, in MOST cases the DCT will easily out perform a 6MT when they go head to head or you compare them at the same track event. You simply need more power in the 6MT to compete, especially before 120. I've seen plenty of Vbox runs to confirm this as well as side by side comparo's. YES a 4-6MPH trap difference is not hyperbole. As spu4ea pointed out the only place where a 6MT has a chance is in the 115 range, up top, below that it's just not a contest, only 1 6MT I ran was close and that was at higher speeds, he had more power, less weight, etc.
Here is a few vids that show the gap -
6MT vs DCT, similar mods, not even close
Here's one that is a tad closer, but the 6MT, made more power than the DCT-
If you want to be even more accurate it's better to compare times from the
SAME DAY. Famoso track rental, here's a 6MT Gintani Supercharged M3 in the far lane, and a very quick 6MT in the near lane, this is the same 6MT that ran close to me way up top on the way to Famoso and even started to slightly pull, but before 120 it's all DCT even with more weight (DR's, tools and jack in the trunk) and less power, displacement.
In the Vid below, both these 6MT's are on street tires, hence the bad launch and lackluster ET's, and I'm sure you could add a few MPH with better traction. At this same event, same day, I hit a 115.3MPH, at full weight and 115.5 with the rear seats out, only around 3MPH less than then the 6MT SC'd M3 and approx. 6MPH more than the N/A Modded 6MT, that had no rear seats and more power, my N/A DCT M3 was rated at only 377whp on a DJ.