Decades ago, Browning (and later, Mauser via Gamba) produced the best of both worlds, in terms of triggers for double-barrel shotguns. Like most conventional guns having double triggers, the front trigger fired the more open bore; the rear trigger firing the tighter choked barrel. But where this trigger system differed from every other double trigger design, once either trigger was pulled, you could pull the same trigger again and the second (other) barrel would fire.
From what I've read, as good as the idea was, the design was expensive to manufacture and, more importantly, prone to malfunction.