Nintil, a libertarian blogger performs a long series of assessments on soviet GDP growth here.
To his credit, Nintil updated the post a number of times as he became aware of new arguments and evidence. Like always in econometrics, there is never such a thing as the final word. With that caveat though, the three headline results to my mind are that the USSR was the 3rd fastest growing country in the world over the period 1928–1970, the 10th fastest growing country in the world between 1928 and 1988 and the 61st out of 148 countries between 1950 and 1989.
The overall record is strong growth in the early phase, somewhat weaker but not disastrous growth later on. Socialists will argue that this record of growth is spectacular, given the opposition the USSR faced from most of the industrialised world and the destruction of the flower of its populace during World War II. Capitalists will argue that early rapid growth was unsustainable, and that the USSR should have done much better given other indicators. Nintil himself argues causes of Soviet growth do not bode well for the system, personally though I find it far more interesting that a radically different structure to a contemporary market economy managed to muddle through at all, to grow and even to grow reasonably well.
Moving along to China we find:

(Graph created using St Louis Federal Reserve Bank Data)
Pretty reasonable growth with a single anomalous period, the so called “Great Leap Forward” . Many have compared its growth favourably with that of India. For example John Ross gives the following graph (using a smoothed five year average):

Notice also that, again with the exception of the great leap forward, there is not a lot of evidence to support the thesis that China was a stagnant backwater until concessions were made to capitalism with the Deng reforms in 1978. I am not contending that the Deng reforms were useless (I’m not contending that they were useful either), but the notion that China wasn’t growing before the Deng reforms is false.
Now let me be clear on what I am doing here. First of all I am not, in any unqualified sense defending the economic record of command economies as better than or equal to capitalist economies. There are counter-arguments to be had, controls and corrections to be imposed by both sides etc., there always are, so I take no position on whether command economies under ‘fair’ conditions grow faster or slower than market economies.
Secondly I’m certainly not endorsing these societies as a model for our own, I believe strongly in the freedom to argue about ideas, politics and values, and for all to have an equal say in the formation of policies, and these societies certainly didn’t provide that.
What I am arguing is that the often made claim, that command economies simply cannot function is clearly false. Some will argue that the performance of these economies was fantastic, others will argue it was poor, what is clear is that these economies can function and grow at a very appreciable rate. A trivial point perhaps, but these days so many people seem to talk as if command economies were literally impossible and unworkable- how quickly we forget the role that they played in the 20th century.
Equally important is to consider these things in a dynamic as well as a static context, anything that can be made to work can be made to work better. It tells us far more that the Wright Brothers flew a plane at all than the speed at which that plane flew. Coordinated economies after all have far more policies that can be tinkered with and improved than the alternative.
What’s more, if there are two different ways of structuring economies- market and command- and both are workable, it follows that there are probably third options, perhaps even options with genuine economic democracy.