If you can hog all the armor on the map, you should have an easy time killing your opponent. Tournament mode is basically identical to a game of deathmatch with just two players. This is a true test of skill because there are no outside forces to interfere with either player's game. Most Tournament games have a time limit instead of a fraglimit, because these games tend to be slower than the frantic pace of deathmatch. Long games commonly end with low scores because the players would rather retreat than risk dying.
Tournament play is very difficult to master.
The most successful Tournament players memorize the timing of every powerup on the level, so they can grab it the moment they pop up. As his opponent waits for the red armor to respawn, a good player can swoop down and force him away just as it pops up, then take it for himself. On public servers, there is usually a line of people waiting to play in the match. The loser of the match gets booted to the end of the line, while the winner stays and fights with the next challenger. Long waits can be common, and many times a person will spend more time in line than they do actually playing.