Do You plan on hunting with smokeless or blackpowder?
Are You planning on hunting large game or small game?
What do Your local laws and hunting regulations say about calibers and impact energy?
In my experience the .45-70 Pedersoli Sharps can be handloaded with smokeless to the velocity and impact energy that is required to legally hunt deer, moose and reindeer here in Norway. (2200 Joule)
The Trap-Door can only be safely loaded to the level required for roe-deer and smaller game. (980 Joule)
Another advantage for the Sharps is that it can be fitted with a period correct long scope, whereas on the Trap-Door the opening of the trapdoor will conflict with the scope, unless it's side-mounted.
One advantage to the Trap-Door is the speedy ejection of empty shells.
If I didn't already own two Italian Sharps rifles, I'd seriously consider the Overbaugh model myself...