Well, right out of the gate, nihilism is what Nietzsche warned against, not what he espoused or encouraged. The better question is if his idea of becoming an overman is similar.

I'd argue it's more similar to Kierkegaard, because striving is, ultimately, an attempt to impose order on chaos. Both of them recognize that that's not really, truly happening at the highest mortal levels (though Kierkegaard obviously posits that the highest level, God, has it all figured out.)

If Kierkegaard is proposing a way to help you make sense of absurdity even if it can never truly make sense to a mortal, Nieztsche is telling you to go out there and make the absurdity make sense - like, with a sword. Be your own boss, and everybody else's. God is dead, so there's a vacuum. Fill it. Be awesome.

One could rightly criticize Kierkegaard's philosophy by suggesting that he's just telling people to be weak and follow what some other man - maybe even an overman - laid out as The Truth by the sword. Of course, Nieztsche's philosophy involves running forever and never stopping, lest everything catch up with you. It's exhausting, and it gels far too well with the general bent of high-functioning narcissistic psychopaths (and even some low-functioning ones, if enough people in a given realm are profoundly dumb and gullible already, cough cough.)