With average service / carry DA guns it is generally slightly slower than SA or striker. Best to best might not differ but on average and by the distribution just a touch slower. Not by a lot and certainly not enough to ever consider thumb cocking.
With a current crop of competition-geared DA/SA guns there is no draw time difference but those guns have DA pulls same or lighter than of stock Glocks, and they weigh twice as much. In general, I don't think that discussing merits or limitations of DA/SA on examples of Tanfoglios or Shadows translates that much, if at all, on USPs, P30s or 229s.
Then there is a newer generation of DA/SA guns that try to bridge form and weight of service guns with trigger qualities of game guns. CZC and Cajun CZs, polymer and alloy, Wilson and LTT Berettas. Depending on the sample, those might be just as fast on a first shot as anything else, although I find that most improvement in those guns is in already good SA pull while DA could vary.