Scenario
I suppose the best idea would be a series of games of which the goal of each game effects the outcome of the next, and so on until at the end of the day their is a clear winner.
However, the goals for each game must be different so that any one team which perhaps has a clear advantage due to experience, firepower, etc, would not necessarily win every game, thus evening out for each team throughout the day.
Most scenario type days I have been too, one team tends to dominate, so a structure of mixed goals, where perhaps a win in one game leads to a disadvantage in the next, might be a good suggestion for a scenario day.
Maybe when I'm sober I could help you with an example or two, but currently the grey matter is fried on Bulmers cider..
Hope this is helpful...