Your essay can be tackled using multiple tactics. First of all, the course of your essay depends on the way YOU define "power." Although the US and USSR both used federal power to combat with each other, they refrained from military combat (a nuclear war would have literally destroyed the planet). For the "global scale" part, I would include how in some ways, the Cold War could be considere international (because containment was a policy in Eastern Europe, the Middle East and SE Asia) but then again, it wasn't to the extent of World War II. Hope that helps!
