I would say generally that the advantage of the 16 over the very light 12 is:

There are a lot more 16-bores available as there were a lot more made.

The 16-bore with a 15/16 oz load throws about as good a pattern as anything.

The 16-bore can be made light without having to be made short or thin to get the weight down, so will be a stronger gun, weight for weight. This is especially the case with the barrels.

16-bore ammo is easier to get and there is a wider range available.

You will have a wider choice of price and quality in 16-bores. I have seen relatively few 2" 12-bores and they have almost all been box locks of lower-middle quality.

My points are all pragmatic ones, I think.