I was torn for a while too on a recent build between leaving the barrel bright, and finishing it.
First you must ask yourself what look are you going for: Do you want your rifle to look like it is 200 years old, or brand new?
If you are going for the old look, you might want to consider browning. If you are going for the new look, then bright or bluing. Guns were both blued and browned 200 years ago, but most of them look "brown" by now. You won't be wrong by browning a new gun, but it may be associated with looking old. Keep in mind that if you are going for the old look, then you ought to be distressing the stock, antiquing the brass, etc.
I went with the new look on a recent build. Used Birchwood Casey Super Blue on both barrel and lock. I draw filed the barrel first, then sanded with 220 paper. I then applied 3 coats of BC, and carded with 000 steel wool between each coat, then rubbed with boiled linseed oil.
It turned out great, but it was a little darker than I wanted, perhaps I should have stopped at 2 coats. People ask me if I charcoal blued the barrel, so for a quick and easy cold finish, I am happy.
The downside with the cold bluing is that it doesn't seem to be as durable. The extra effort of applying a charcoal or rust blue may be that it's more durable. But, that didn't matter to me, because I want my barrel to age and naturally take on a petina.