"If we are considering the same shotgun model for conversion and have a 12 ga. or 16 ga. to choose from, is there a benefit to using a 12 ga. frame if the cartridge will fit into the 16 ga.? Is there a downside to using the 12 ga. in such a case? "

This all depends on the cartridge that you intend to build the rifle in. I build a lot of .450NE sized doubles and feel that the weight should be between 10 and 11 pounds to make the recoil manageable. While a 16B can be used, from a strength stand point, it is hard to get the proper weight. My first .450-3 1/4NE is built on a 16B frame, has over 900 rounds through it, and is still tight, but it only weighs 9.5 pounds - a bit light. Anything bigger than a .450, (500/465, .470, .475, .500) really needs to be on a 12B frame. The .500 is a another break over point - it can be built on a 12B frame, but may end up being a bit light for the cartridge. I feel that a .500 should weigh around 11 pounds, or a bit more. Anything over .500 (.577), needs to be on a 10B frame.

Ellis