One factor affecting the desirability of the 16 in a SXS is that typically it is less expensive to acquire than a 20 gauge, but often weighs the same or less than a 20. I have 3 before or between the wars Birmingham boxlocks that weigh between 5 lbs. 12-13 oz that were acquired for slightly more than a 12 gauge,but considerably less than a 20, fit and finish equal.
In the past few years looking at French auction sites, I note far more 16 gauge accessories listed than 12 or 20 gauge. That, to me, is an indication of the popularity of the 16 in France.
While one of the Birmy's was re-proofed for 70mm, I hesitate to shoot the 2 3/4" 1 oz. loads because of the age of the gun and wood. I am content to either handload or shoot Polywads, handloading either 3/4 or 7/8 oz loads. I use the cheaper Herter's 16 gauge 1 oz. loads for dove and snipe shooting them out of my Ithaca 37's or M12.
Gil