I was originally under the impression a bit of research would reveal the answer but the general view appears to be each were building in self defence. Being brought up in western society I have always been under the impression the Soviets warmongered but is this the case? Thanks. Edit: sorry, I was referring to eachsides propensity for starting proxy wars.
Are you referring to NATO - Warsaw Pact arms buildups during the Cold War or are you asking about each sides propensity for starting proxy wars?
It depends, the Soviet Union fought in WW2, but that was a defensive war for them. In the Russian Civil War (1917-1922) the SU nearly conquered Poland, but that was only in response to an invasion by Poland. The SU did conquer the Baltic states (Lithuania, Latvia and Estonia) and parts of Romania (Bessarabia) and Finland (Karelia) as a part of the Nazi-Soviet pact on 1939.
From then on, the SU was relatively peaceful, confining itself to supporting communist insurgencies and states whenever they cropped up. One example of this of course would be Cuba, which would neaerly bring the two Superpowers to war with each other. The only exception to this was the Soviet invasion of Afghanistan (1979-1989), which would help bring about its fall.
So over the course of 80 or so years the Soviet Union fought 6 wars where they were the aggressor, the vast majority of which happened before WW2. So not really.
Granted, this excludes proxy wars.