Seriously, it depends on a number of things. I'm assuming you're talking about playing in tournaments like most weekend travel ball tournaments.
Pool games are more important in some tournaments than in others. For example, in some tournaments, pool play determines which teams advance and which don't. In other tournaments, all teams advance and pool play only determines seeding. In that case, who the other teams are determines whether seeding is even important. If there are some really good teams that you'd prefer to avoid in the first round of the bracket, then you need to put more emphasis on doing well in pool play.
If pool games are deemed unimportant, then you can use your lesser pitchers in pool play, let them get some game-time experience, and save your best pitchers for the games that matter.
The schedule for the tournament also figures in to your decisions. If you're playing in a 2-day tournament, then you have less flexibility because there is no chance for pitchers to pitch significant innings in multiple games AND get proper rest in between. If, on the other hand, you're playing on a 3-day weekend, then you have the option of throwing your best pitchers a limited amount on the first day, giving them the second day to rest, and then bringing them back to throw more on the third day.
The number of pitchers you have also figures into the decisions. If the pool games aren't that important, then use your lesser pitchers to pitch by committee and chew up innings. You can even use your better pitchers to pitch by committee and limit them to about 25 pitches.
There are probably other factors I'm not thinking of. But keep in mind that no matter how well you plan, things will rarely go according to plan. So make sure you have contingency plans.