The reality was at that time, that neither country could go to war but had no real idea whether or not the other was in a similar position.
The problem here is one of sustainment.
In military thinking, sustainment is the ability of a nation to continue to pay for military action on a given scale over a defined period. When the Nazis invaded Poland, the resulting war was existential in nature. That is to say, France, England, Australia, the USA, were all fighting an enemy that intended to strike them and either destroy or completely occupy them. In such a situation, money is always found to fight such an enemy because economic futures only have to be worried about if there is a future to worry about in the first place.
If you look at Australian defence spending during the early 1940s for instance (apologies but this is the only country that I have numbers for off the top of my head) it was spending around 40% or more of GDP per year on its military engagements. That is completely unsustainable beyond a couple of years. Admittedly Australia at the time had a very small military at the beginning of WWII and ramped up in aircraft building, troop numbers, and many other military ventures as a result of finding itself in a war in two theatres (European and Pacific) and as such is probably an extreme case, but the truth is that the other nations embroiled in WWII were also quite strapped at the end of it economically.
Russia was even strapped DURING the war. At Stalingrad, they didn't have enough rifles for all their soldiers and the only reason why Stalingrad held was that the Germans were completely unprepared for Russian winters.
So, it was actually a good thing that the war ended when it did. Part of the reason why there was an Eastern European bloc during the cold war was that the Allies didn't have the resources to drive Russia back out of Europe, and Russia didn't have the resources to drive further west into Europe.
Who would've won? Whomever had the better command of their resources at the time. Given that the USA and Australia were always likely to have to pull out to finally deal with Japan at the time, it's possible that Russia would have taken all of Germany, and possibly even more of Europe, but in reality we'll never know because both sides were really hiding their economic positions too well. The cold war was a cold war for a reason when you realise no-one could afford a hot one.