I have found that most folks who shoot double triggers a lot, and have for most of their life, including myself, still require some concerted practice to be able to shoot the left barrel first, then move to the front trigger with the same speed and "second nature" that we do when firing the right barrel first, then moving to the back trigger.
As much as we like having the instant option to choose barrels (chokes) by choosing a trigger, I would bet money that most of the shooters who champion the double trigger set-up cannot go from rear trigger to front with the finesse of front to rear, just from lack of practice. True pairs on a sporting clay range will give us that practice we need.