Yes they are very close. Their interpretations of the Greek conflation of happiness and truth, the impulsive blond beast, critique of Christianity, etc...are both very similar.
When Stirner wrote that the Greeks arrived at a realization that there are no natural predications, Nietzsche at the same time claimed that the Greek morality (Master morality) arrived at Nihilism. Interesting to see a recurring asceticism coming from and evolving into nihilism. Another problem is the idea of man as natural, well then I guess there would be natural predications, analytic truths, synthetic a priori? It is troubling to reconcile and weigh the arrival nihilism....
Feuerbach, Stirner, R. W. Emerson, Heraclitus, and Schopenhauer are the best thinkers to consider when you're looking for a Nietzsche exegesis (Kropotkin).
As for the communist fraternities, Communist economies do not work. I can't name one successful "Communist" economist or country that did not eventually except the truth of a mixed economy. I am not a neo-classicist, nor a communist, nor a demo-socialist, nor a capitalist...the best economy is the mixed economy. We don't need to abolish the wage labour system or marriage to avoid group think and the mind slavery of the commune. Just install subtle policies to unmask the deception of the goods markets.
"Life's but a walking shadow, a poor player
That struts and frets his hour upon the stage
And then is heard no more: it is a tale
Told by an idiot, full of sound and fury,