I shoot the tighter choked barrel first a great deal of the time on doves, either the left barrel on my S x Ss or the bottom barrel on my superposed 20 ga. Beretta (I like shooting the bottom barrel first on an O/U, so I choke it tighter accordingly). The reason is that I love incomers on doves best of all. It is fine sport to test one's self to take an incoming dove out of a drove with the tighter choked barrel, at a good distance, so that the second barrel can double on another one of the incomers at closer range. Having both fall in front of you is great sport, and not easily done by a novice dove shooter.
All my S x S guns had the left barrel choked tighter, originally, but then I only have one English gun.
SRH