It probably depends on what the conflict is, but overall I believe the emphasis should mostly be on individual rights. Individualism allows a person to maintain their distinct personality and personal rights whereas collectivism forces people to sacrifice their freedom for the "greater good". Achieving the common good by neglecting individual rights often has disastrous consequences, Nazi Germany for example.
I would pick collectivism, but collectivism usually does nothing besides pit larger groups of people against each other under one ideal or banner. Even if a collectivist group starts off with the best intentions, they usually devolve into a bunch of loud mouths where the fringe folks gain most of the control.
I believe that it is important to put value on individualism not just during conflicts but anytime. Individualism is important because it can give you a different perspective. Seeing things from someone elses point of view, expecially during times of conflicts is important. It is important to remember that the collective thought is not always they right one.
I feel that during a time of conflict is when it is most important to put the group ahead of the individual. People thinking about what is best for them individually is often not what is best for the group as a whole or even themselves in the long term. During times of conflict groups are more likely to solve problems than single individuals, regardless of their abilities.
It depends on the conflict. In cases where it involves a lot of people, such as human rights or a labor dispute, then collective bargaining is the best way to resolve the problem. Individualism in such instances typically only gets in the way, and leads to bickering and fractured ideologies.
During a conflict, we need to value collectivism. The two sides need to argue it out, then come to a compromise, and join together as one so that they can become stronger that ever. Look at what happened after the Civil War with the US, we are stronger than ever.