The forces of the Red Army and Red Air Force was larger than the US Army and US Air Force during the Cold War (except maybe right at the beginning). The Red Navy on the other hand never came close to the US Navy in size, except for the submarine service.

The USSR had three year conscription, which ensured that their standing army and trained reserves were larger than America's (note that the USSR's population was always larger than America's). They also mass manufactured military equipment in great amounts, sometimes in astonishing amounts. For example the number of T-54/T-55 tanks comes to at least 86,000 (though not all made by the USSR). These tanks were also the best in the world when introduced, sparking the introduction of a slew of new NATO tanks in the 1960s, which in turn where matched by the T-62 and T-64. For comparison their total numbers exceeded 25,000 compared to 15,000 M60s.

The Soviet Union was capable of maintaining technological parity for much of the Cold War (more precisely the advantage see-sawed back and forth as new equipment was introduced). It's not really until around 1980 that America's and Western Europe's advantage in electronics tips the balance decisively in favor of NATO. Widespread use of computers allows great advances in research and development, as well as providing military platforms with equipment that enhance their capabilities beyond their raw performance metrics. The USSR never came up with something as good as the M1 Abrams, though up in the air the MIG-29 and SU-27 were roughly equivalent to the F-15 and F-16. Fortunately American pilot training was superior in the 1980s as the training system was revamped following disappointing performance in Vietnam. There were of course areas in which America always had an advantage, such as logistics, but generally speaking WW3 could have gone very badly for NATO, even without nukes flying around.

However, if WW3 would last long enough, then mobilization of industry would certainly ensure NATO victory in the end. The first world was simply superior in economic output compared to second world countries.