Typically, the left barrel has a tighter choke (if there's a difference at all).   That method would fire a tight pattern at the game first (when it's closer to you), and then send an open pattern out to meet the missed bird at a longer range.  
 
...but that's what spreader loads are for. 
 
I'm fortunate to own a petite German drilling (16 x 16 over 9.3x72R) that has hammers that I can actually cock simultanously.     My Parker 12 g. hammer gun - that's an extremely difficult task;  and with my Dougall hammer gun - that's an impossible task. 
 
             (Maybe I need a bigger thumb ?)
		 
		
		
		
		
		
		
		
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