Immediate thought is that VP will be a more important position--de facto leader of the Senate (whatever the rules might say), or at least the Administration's conduit to Congress. So it will be important to have someone who will agree with the President, rather than using it purely to advantage in the campaign, and someone who can work well with the Senate. Lyndon B. Johnson would (under this system) be perfect for the JFK administration except for the little detail that he and Kennedy didn't get along at all, for example, but Sarah Palin would make no sense--she obviously would be ineffective in that role.