Could you clarify whose perception you mean? For example, the Soviets themselves would naturally encourage the view that they were stronger.

I think you need to be more specific with your question in terms of time frame and scope.

However my intuition tells me you mean military might in terms of fielded manpower, ability to produce equipment and the ability to launch an threatening offensive into own or allied territory.

I can only speculate how it was perceived, but I can tell you that they were way stronger right after WW2. The soviet populations and armed forces were extremely mobilized and you had not only a horde of several million army personnel directly on Germany. This force was also well equipped and battle hardened. It is true that the Soviet army suffered unsustainable loses in 41 and 42. The the every increasing reconquest densely populated assured a never ending stream of fresh reinforcements.

After the capitulation of Germany there was little in the way of the Western allies to contain the soviets and this threat was apparent. When plans for preemptive strikes that would involve former Wehrmacht forces were evaluated.

Fortunately, the Soviets rather licked their wounds and established a series of bufferstates that aimed to contain the weakpoint in Russian Geography that is the great eastern Europe plan.

As when the balance shifted is hard to say, given the vast mechanized formations and the nuclear deterrent.

Personally I would even argue it only really shifted after the demise of the Union. This however starts to enter the realm of speculation and I will refrain from it.