I've done a few campaigns that were competitive with mixed success. Of course, any game with a high death rate or guaranteed conflict (Stormbringer, Paranoia) makes for a good choice.
The largest honest RPG was a Vampire: the Masquerade campaign that peaked around 30 players, although only about 10 full-time devotees. This was in college and I had loads of time to spend on it. It worked well for about 8 months and was based on a few key drivers: (1) the current prince / ruling class in Chicago (the setting) was gone / lost and there was a struggle for power (2) there was an astronomical event of great importance which happened to basically coincide with the date of the council which would determine the new Vampire leadership (the council would be meeting for a solid week, the convergence was on day 2).
We had a good mix of players and characters including some vamps, some hunters and some werewolf characters (and about 5 oddballs - normal humans, ghouls and one mummy), but mostly because there were NO direct confrontations. The basic rule I had was, unless both PCs were there, they were generally unavailable for direct conflict. Instead, henchmen, hirelings or friends were the bait and since Vampire is a game where quite easily a stronger combat vamp can be the henchman of a weaker, mental-dominating vamp it worked out well. I have to say it was one of the best groups to deal with because we had virtually none of the "every RPG must be comical" or "I am my character" types in the game. They were all mature, or at least cared enough to pretend.
The final culmination was a giant live-action new-years party at my house with about 90% of the players, full and part-time, showing up. There were additional rules then, but basically the game had quite a few ambushes of folks in small closets where direct confrontation worked itself out. One group managed to get their TNT (all props represented by index cards) through the search at the front door (I had assistants helping with the game resolution of search / hide / etc.) and blowing the place nearly to hell at the stroke of midnight. At that point, the game was off and everyone just got their drink on. We worked out survivors and the outcome during the next week (the assistant storytellers kept track of where folks were at midnight.
Those that lived (either because they left the house or bomb vicinity...or maybe were just that strong, etc.) determined the course of the city, then a smaller group remained and the campaign continued for a few months with a normal sized group (6-8).