changing it once or less than once per week seems like the best option, as it allows enough time for players to become familiar with the mod, even if they've never played it before
pandering to people who only want to play their "favorite mod" is counterproductive to the growth of the community, as these are the people who are least likely to stick around. i think the difference between someone who plays for 5 months and someone who plays for 5 years is knowledge of the game. if someone wants to play a particular mod with friends, they can make a room or join a public room. if they want to play it competitively, they can duel.
changing the tournament mod less often will encourage people to continue playing toribash for longer because, in my experience, the more you know about a game, the more likely you are to keep playing it. tournaments are the ideal environment for learning because there is a high reward for winning and no cost for losing.
while changing the mod every 2-3 days will expose people to more mods, it does not allow them to learn very much about them. public and qi-restricted public servers are good for exposing people to mods and allowing people to play their "favorite mod"; tournaments are much more valuable as a learning tool.