My smaller carbon steel cannons/mortars have all been either blued or painted. I've thought about Parkerizing since I do it at home but haven't done one yet.
Thing is, if you're going to use them they're generally going to get a lot more beat up than your favorite rifle ever would. Especially so if you're talking about a larger cannon since you have to man handle them during transport and use. They're gonna get wet from swabbing and will have corrosive powder residue all over the place. If you don't care for "patina" and battle scars, paint is best because it's the easiest to do over (an over and over) again. It's also cheap, easy and good for keeping a cannon stored outdoors from rusting.
I'd be way too lazy to go through what would be required to properly clean and lube a full size blued gun to keep it from rusting up after firing it. Bad enough just doing my BP revolvers.