Have played in quite a few friendly competitions for both Ancients and Napoleonics C&C here in Melbourne. The Ancients is usually Romans versus the rest with half the player using various Roman armies and the "Barbarians" using anything else. There's an overall winner for each side and overall "Team" winners (i.e. Romans or Barbarians).
The Napoleonics is usually organised with multiple tables set up for phases or flanks of the same battle and each player doing their bit and the scores deciding whether the French or the "Others" won the scenario. and points are awarding accordingly. In one game I won a "Marshal of France" title as we (as French) broke through with a big win on our right wing against the Russians (which we historically did not) whilst our fabulous Guards divisions failed on the table to our left. Consequently, the Umpire awarded us victory laurels because, despite our Guards failing, their Russian opponents were fought to exhaustion and the Umpire decided that my successful right wing attack would have rolled up the flank.
Such imaginative use of the game makes these events amongst the most enjoyable wargaming events I have played in. The competitiveness is about the whole round of games and teams, not individuals. However, it was terrific to become a Marshal of France, if only for a game or two!