The Allied GI is stronger than the Soviet conscript, but the Soviets can produce more conscripts faster and at a lower cost. The Soviet rhino, however, is more powerful than the Allied grizzly, and the differences are balanced by the cost. Counter the Allied cheaper tanks with bruising tanks of your own. Each country should deploy its unique unit to assist in the battles. For instance, the Iraq desolator is supreme against enemy infantry, and Russia's tesla tank is one of the more devastating units in the game.
Numbers are extremely important, as are power and strength.
In long games, the Soviets can take advantage of the cloning vats and produce more units in less time. Don't neglect the usefulness of a pack of terror drones. The units are hard to attack and can rip through enemy infantry and tank groups in a matter of seconds. Lead into battle with other units and follow with the terror drones. The leaping and quick attacking action of the drones should provide a numbers advantage, ensuring victory in a closely contested battle.