Power is used in the game for different reasons. Without power many defensive structures do not work and mini map is no longer visible. Robot Tanks also, will shut down and won't be able to move until power is restored.
There are only a few buildings that grant power but can be built multiple times to provide more. Most of the rest buildings consume either a minor amount or a major one. Power is very important so try to keep it running. A building that provides power will provide less as it get damaged.
The Allies have the Power Plant which costs 800 resources and provides 200 power. It is the only structure the Allies have for power and since they have plenty buildings to support they need plenty Power Plants which are quite costly.
The Soviets have the Tesla Reactor which costs 600 resources and provides 150 power. It's a perfect structure for the beginning since it is constructed quickly and cheaper that the Allied Power Plant. The soviets also have the Nuclear Reactor which alone can hold an entire base running endlessly with power as it grants 2000 power for the mere cost of 1000 resources which also is not limited to just one. A Nuclear Reactor is enough to keep all 6 Super Weapons running at the same time. Lastly, a Nuclear Reactor will explode upon destruction so it can cause major damage if built deeply in the base.
Bio Reactor is the same as the Tesla Reactor. It costs 600 resources and grants 150 power. However, Bio Reactors are quite better and can actually prove much better that the Power Plants as well since you can garrison up to five infantry units for extra power. Each unit, regardless of cost or strength will grant an extra 100 power, thus a fully garrisoned Bio Reactor can provide 650 Power. Two or three of those can be enough to let a base running with no problems. Mind Controlled units can be Garrison inside Bio Reactor but if the Bio reactor is destroyed the controlled unit will no longer be controlled since upon entering the structure it is freed from mind control.
To sum up, the Soviets obviously have a clear and big advantage with the Nuclear Reactor. A single structure that grants massive amount of power, is very durable, is very cheap and is not limited to just one. the only drawback is the explosion it causes upon destruction but the building is one of the strongest in the entire game.