Great question!

The Soviet Union, as a command economy, was very, very good at marshaling the nation's resources towards major goals, particularly ones that included major, industrial qualifications. As /u/Entropius said, the USSR was first in many of the important space milestones, though of course the United States eventually caught up and beat the Soviets to the Moon. But the Space Race is only one part of a much larger picture. We modern Americans tend to discount the USSR as some sort of born-to-fail concept, but that is to belie the very real fears that our parents' and grandparents' generations often held about the Red Menace, particularly in the darkest moments of the Cold War. After all, if the USSR was doomed from the start, how did it persist until 1991?

First, understand that the Soviet Union was not just a Cold War entity. Getting its start late in 1917, the Soviet Union's Five Year Plans changed the nation from a relatively backward, agrarian (albeit slowly industrializing) society to one of the most modern industrial economies in the world. Though it is hard to be sure exactly how fast Soviet production was growing (due to profuse number-fudging in many sectors in order to meet targets), by 1939 the Soviet Union was assuredly far more developed than it had been at the beginning of the previous World War. I cannot provide you hard data for this, unfortunately, as many of the supposedly "adjusted" or "authoritative" statistics of Soviet pre-WWII growth were retrospectively created by organizations that did not exist before the Cold War (ie. the CIA).

What I can tell you, however, is that the Soviet Union's first and most important advantage was its capacity to fight total warfare. The Great Patriotic War of 1941-1945 is, by some estimates, the most brutal, costly, and lethal war in human history, even if every other theater of World War II is removed from the equation. One must understand the cost of the Soviet victory on the Eastern Front: not only was the Red Army fighting the Wehrmacht (probably the best land army in Europe at the outset of Operation Barbarossa), they were fighting that same organization, backed up by all the resources of a subjugated Europe, and supplemented by hundreds of thousands of additional troops supplied by German puppet states and allies. Despite the huge cost of the war to the Soviet Union, with some casualty estimates ranging up to 30 million Soviet citizens -- perhaps over 15% of the entire nation's population -- the Red Army was far and away the biggest factor in the defeat of the German Army. Years ago, I was told by one of my professors that the Soviet Union was responsible for the deaths of eight out of every ten German soldiers killed during the war, a statistic I have never since been able to disprove. One might argue about the strategic impact of the Allied Combined Bomber Offensive that helped to knock out Germany, or of the impact of D-Day, but by-and-large these contributions were designed to limit the logistical abilities of the German Army wherever it was fighting, which, of course, was primarily in the East. It is an old mantra that boots on the ground are the only way to win wars, and the Soviet Union was able to suck up huge losses and keep throwing men and materiel into the fight until their boots stood on German soil. That's a hell of an achievement.

Beyond the victory of 1945, however, the Soviets were very good in the soft power sphere throughout the 1950s and 1960s. At a time when Europe's colonial empires were breaking up and newly independent nations were given a choice in their future, many chose Soviet Communism as the guiding light by which they steered their ships of state. The Soviets promised a new order of business, a total polar opposite from the American system, which looked a lot like the capitalist democracies that had colonized African and Asian nations for so long (an image not helped, by the way, by America's involvement in overthrowing Central American governments or the War in Vietnam). For some time, insurgent groups and major nations alike turned to Soviet Communism as a way to recover from the destitution and humiliation of their colonial pasts. Even today, now that the Soviet Union is dead and gone, the myths ascribed to "freedom fighters" as diverse as Che Guevara or Gamel Abdel Nasser or Ho Chi Minh are a reminder of a time when the Soviet Union actively supported and underwrote nationalist and collectivist movements around the world. It was not until the 1970s that the flaws of Soviet economics would begin to show plainly for the world to see, and not until the 1980s that the United States could confidently say it was winning the Cold War.

But one should not underestimate Soviet hard power either. The Soviet Army during the Cold War period was probably the largest and strongest in the world, perhaps rivaled only by the People's Republic of China, and I would argue that the former was immeasurably better equipped and disciplined than the latter. The Soviet Union also retained a very sizable nuclear weapons stockpile, surpassing the United States by the 1970s. Both of these things, as you might imagine, required a sizable industrial infrastructure to arm and supply. This brings us to another advantage of the USSR: arms production. For quite a long time, Soviet weapons appeared everywhere in huge quantities: they were cheap, reliable, and easy to operate. The Kalashnikov rifle is only the most famous of these; systems like the RPG-7 anti-tank weapon, SA-2 "Guideline" surface-to-air missile, T-55 medium tank, and MiG-21 fighter aircraft were ubiquitous in almost every civil and colonial war around the globe for decades. In addition, Soviet military advisors could be found almost anywhere their weapons went, giving a huge boost in discipline and effectiveness for pro-Communist forces around the globe.

And, finally, we come to the most nebulous of all Soviet attributes: the intelligence services. The KGB and GRU throughout the Cold War were highly effective agencies, infiltrating the upper echelons of many Western governments and intelligence services for decades. It is often said that Soviet intelligence was a far more capable organization than their Western counterparts, and while that is not a hard-and-fast rule it can be accurately applied to certain eras or nations throughout the era. Soviet intelligence was very good at discovering idealistic individuals at the upper levels of Western governments who would turn over hugely damaging amounts of information on a routine basis. People like the Rosenbergs, Alger Hiss, Kim Philby, Gunter Guillaume, Aldrich Ames, and John Anthony Walker all sold huge amounts of information to the Soviet Union, often for a pittance compared to the damage they did. Though we cannot know exactly how many Western defectors and suppliers existed on the other side of the Iron Curtain (often because these documents remain classified), it seems that the Soviets were at least as good if not better than Western agencies in this respect.

The obvious caveat to all of these is the human cost, which was often very high even by contemporary standards. But from a purely empirical standpoint, especially considering their underdeveloped starting point, the Soviet Union definitely outpaced the West in these areas.