An advantage of DBIx::Connector is that if a handle falls over (the connection drops) the connector will re-establish a connection automatically, so you don't have to solve that problem yourself. Eventually you're going to solve this problem one way or the other. DBIx::Connector allows you to not have to solve it with code that you will then have to maintain yourself.
But it's not right for every use case. Sometimes you really may have a good reason for solving it with your own code.