In large samples the error bars for the median are sqrt(pi/2) times the error bars for the mean if the underlying distribution is normal (the link gives more general results, but that helps give some intuitions about being directly comparable)

https://en.wikipedia.org/wiki/Median#Sampling_distribution

It works the same way. Nine times the clocks, three times smaller standard deviation for both the mean and the median of their readings. In a normal (and any symmetric) distribution these two are the same anyway, so their difference will tend to zero as you increase the number of clocks and the measurements from a single reading of all the clocks look more and more like a bell curve. This is asymptotic behavior so the "rejects the outliers better" aspect does not come into play, and I do not know whether it is useful in this situation or not.