There are at least two major advantages to having a vice president who has real duties. First, the vice president can add his (or someday her) talents to the executive team. Nowadays, vice presidential candidates are often picked explicitly to be helpful in terms of politics or policy. The last three vice presidents, Al Gore, Dick Cheney, and Joe Biden have all been important parts of the administration and have brought real talents to their positions. Second, having a vice president who does serious work makes it more likely that the US will have a good president if the president dies. This was particularly noticeable when President Kennedy was assassinated and Lyndon Johnson stepped in to the office.
There is not really that much in the way of negatives associated with having a vice president who is more than a ceremonial figurehead. It is possible that policy conflicts will arise between the president and the vice president, thus reducing the cohesiveness of the executive branch. But this has not been a problem to this point. Thus, the advantages of this system definitely outweigh the potential problems associated with having a meaningful role for the vice president.