I like them both, for different reasons. I feel everyone should try the BB at least once, if it's not your thing then fine but the dining experience is amazing. It's a very cool feel in there. Especially if you go during the day, you go in from the sun and you dine at night in the bayou, very cool.

The MC sandwich you get at BB is the same as the regular one you can get at CO, but CO also offers a cheese only MC. At BB you get a full meal, you get rolls to start, you get a salad or a cup of gumbo (super good) and you get your meal plus sides, delish scalloped potatoes and usually asparagus and brocollini. At CO you get no starters (unless you order an appetizer) and no sides, just the sandwich and you go get a small bowl of fruit so I guess that's your side.

If you decide to skip BB and go to CO get the Pomme Frites, they are sooooooooooo good, I tried the ratatoulle last time (first time ever) and I loved it!!!! And CO has Mickey benigets which are delish!!

CO is also cheaper then BB.

So I guess it just depends on what you're wanting, if you just want the MC try CO and get the Pomme Frites to start, yum yum!!
