The MPC command by evaluating the future dynamics of the system, allows to take into account time delays, oscillating systems and non-minimal systems, unstable systems. . . etc. in the presence of input and output constraints and is easily expandable for multi-variable systems. In short, the advantages of predictive control are to reduce the variance (more precision and optimality), to be able to change the setpoint (more degree of freedom in the control of the systems).
The answer strongly depends on the specific application!
We recently published this article
Article Model Predictive Control (MPC) for Enhancing Building and HV...
where you can find our point of view about benefits and drawbacks of using MPC for building energy managment (compared to baseline controllers), in the "Critical Discussion and Conclusions" section.
It can be extended to other energy-related application.