Actually, white oak has more tannins, though there are differences between sap/heart wood which makes relying on the natural tannins a fair amount of guess work.
I'm not sure of the chemistry between the tannins and ammonia/Iron acetate, but I'd assume that either will convert 100% of the tannin given sufficient time. I have got a very "pure" black with both, but nice thing about the ammonia is the depth of penetration. Helps prevent sanding through the color.
Either will work well, I do a lot of fuming so I have a 30 gallon tub that acts as my chamber.