A champagne cocktail is typically made with a sugar cube that's topped with bitters, then the champagne is poured over top. You can also add a twist of citrus like lemon, and garnish with some lemon peel. It has less orange flavor and more of a light citrus flavor.  Classic mimosas are usually made with just champagne and around 1/4 to 1/2 of the cocktail is orange juice. A classic mimosa is typically sweeter than a champagne cocktail with more of a fruity flavor.