What was each side more proficient in on an individual basis?
How did each's specialty soldiers (ie airborne troops, special ops, sniper crews) stack up?
Note: late Cold War is (in my book) late 70s to end of the Cold War.
The U.S. Army was, by that point, a professional volunteer force, where the Pact armies were conscripted. That, theoretically, would provide a slight qualitative man-to-man advantage for the Americans. Also, the Soviet service period was only two years, compared to the American minimum of four, so the American troops would be, on average, more experienced. In Victor Suvorov's "Inside the Red Army", he points out that at any given time, one quarter of the soldiers were in their first six months of training, and one quarter were waiting out their final six months of service and usually none too inclined to work very hard. This, of course, depends on how much credence you give to Suvorov.
The counter-argument to this is more institutional than man-to-man. Modern warfare has demonstrated that it consumes front-line troops at a ferocious rate. Once the American army gets thinned out by combat, they have to resort to the (relatively) small pool of reservists and National Guard. After that it goes to a draft of civilians with no military background. The Soviets had access to a much larger pool of former conscripts who'd had at least some training and could (theoretically) be plugged back in to service more effectively. In a protracted conventional war, there might have been a period where American troop quality deteriorated much faster than the Soviets. Whether this would have mattered is dependent on other factors, of course.