Is running a design at 200 MHz for a longer period of time better than running the design at 1 GHz for a shorter period of time from the power point of view?
If the same voltage is used in both cases, then the dynamic power at 200 MHz is 1/5th of the power at 1 GHz. However, the energy consumed to run the application is the same. The static power (leakage) would be the same in both cases. However, power can be significantly reduced (quadratically) if voltage scaling is applied. If V1 and V2 are the two voltages used in each case, the dynamic power reduction will be proportional to (V1/V2)2 approximately. The reduction in voltage will also result in a reduction of static power.