Neither is more important. A relationship goes both ways. And as for what to do there? There is so very much to do. How can anyone say there is nothing to see? Nothing to do? I was busy every day I have been there.
So, no, it is not more important for her to go first. In fact, it is more important for the relationship, from my personal experience, and from every girl I have heard to visit the girl in her homeland first. Only a few rare exceptions to this.
But then, yes, she should also visit. You cannot make a decision on only 1 visit. Impossible.