It depends entirely on that unknowable reason why someone is killing themselves. If it is due to depression, that is hardly that person's fault, if they have psychological problems, so it cannot be classified as either, though it must certainly take some bravery. If a person chooses to die because they want to see what comes next - I'm not sure if there has ever been a recorded case of suicide because someone was overly curious, but let's go with it - then that would have to be an act of bravery, among other things, because that person has overcome their fear of the unknown, and is willing to take the risk. If someone kills themselves because life is too hard, and they don't want to tough it out, that is cowardice, though, again, it requires bravery. It seems like there cannot be a suicide without both of these qualities.
As for how we could know which quality is predominant in a specific case, it seems that it is for the person committing suicide to decide. Even if that person leaves a perfectly accurate description of why they have killed themselves, others may decide for themselves which they actually believe it to be. I think if a person believes, in their heart of hearts, that they are being brave by ending their life, then no one else can say otherwise.