The 1300 series barrels will work with your 1200. Even if the 1300 barrel will handle 3 inch shell you can still use it on your 1200 but you won't be able to shoot the 3 inchers, only 2 3/4 inch shells will work.
I replaced a barrel on a sears model 120 which is nothing more than a Win 1200. I used a Winchester 1300 barrel and that gun shot 2 deer this season.