Yes, both men and women should participate in the same group counseling because they often share the same viewpoints. However, I think that they should only do these sessions if they are comfortable in sharing with the opposite sex and they feel safe in these sessions. Overall, I think they should be together.
Men and women should participate in the same group counseling sessions for certain things dealing with the realm of counseling. However, we should note about this issue that we need to make sure that all members in the group are okay with this. Also it may be deemed not good for certain things.
I do not believe group counseling is the best method for all people and some people may not find it beneficial. When people do find it helpful, I think it is possible to mix men and women in counseling sessions. I think this really depends on the goals and the problems being addressed. There is no one right answer.
Men and women should participate in separate group counselings because they will be more comfortable without the opposite sex in the room. The emotions and mentalities of the sexes are also different, and they should be counseled with having this in mind. After this, the men and women can come together in their own area of life (such as home), and function better because the counseling had been tailored to their sex.