Well, Primary active transporters require ATP to perform their function. For example, they can be used to pump ions out against a concentration gradient to establish a new electrochemical gradient across a membrane. The secondary active transporters do not require ATP to function, BUT they rely on a previously established electrochemical gradient to function. So indirectly, a secondary active transporter needs a primary active transporter to establish its gradient for it to work later on down the road. This is why the terms are "primary" and "secondary" to begin with. Secondary active transporters operate by allowing a molecule to travel into a cell "up" against its concentration gradient by coupling it to another molecule which is traveling "down" the electrochemical gradient that you established earlier with the primary active transporter.
If I was to say that there was a disadvantage to primary active transporters it would be that they use ATP which is a very general energy source. By creating electrochemical gradients using a variety of different molecules in secondary active transporters, you can create a whole serious of specialized pumps that will only operate when the necessary molecules are present to couple with the gradient you established. It just allows for more control and diversity to establish specialized secondary pumps that can ultimately function whether ATP is present or not.