If I had to choose one, I would say convergent validity is slightly more important first. The reason is simple: the items in one construct need to work together and measure...
If I had to choose one, I would say convergent validity is slightly more important first. The reason is simple: the items in one construct need to work together and measure the same idea before we compare that construct with others. For example, if a scale for speaking fluency does not show good convergent validity, then it is hard to trust the construct itself.
Discriminant validity is also important because it shows that different constructs are not overlapping too much. However, I think convergent validity comes first because a construct needs to be internally clear before we check whether it is different from other constructs. If convergent validity is weak, the whole measurement model becomes less meaningful.