I think we get a little of both type matches depending upon where you shoot. Accuracy can matter more at some matches and the ability to 'run the gun' matters more at other matches. Some matches reward both skill sets.
Sunday Sharyn and I went to a match that had a stage with 5 standard pistol targets at about 5-6 yards with a ~3 inch by 3 inch 'bonus' target at the same distance. It also had 5 standard rifle targets at about 12-13 yards, with a ~3 inch by 3 inch 'bonus' target at the same distance. Five rounds on the standard target, then dump five on the bonus target for a 1 second bonus for each hit. To be successful you needed to be able to run the first five at high speed, then back off a bit for the 5 round dump.
IIRC the stage winner shot that in 17.54, with 8 bonuses taking it down to 9.74 total time.