I think that the central similarity between Kiekergaard and Nietzche is their rejection of the idea of meaning as being solely the content of concepts arrived at like the ideas of geometry. I think they rejected a certain notion of God as a kind of supreme Idea in all of its implications. They instead believed that through living itself only did meaning come. I think that that is why they are labeled "existential".
BTW I don't think that level of reasoning is very useful ultimately. I think the distinction is artificial.
It has some utility however. Everyone has met (or is aware of) the kind of person for whom religion is reduced to theology and whose life shrinks down while his intellect grows. Someone for whom there is no engagement and for whom the truth of God or religion is a kind of knowledge that is general, and even universal purely with no specific application in their lives. Both rejected that kind of intellectualizing. Both men believed in having boots on the ground spiritually - or at least railed against not having them. (You can argue that the mere fact of their writing philosophy disqualified them from the purest of existential credentials.)
Kierkegaard did it without rejecting religion completely. Nietzche rejected not only religion but any system of absolute meaning (including perhaps - shades of Wittgenstein - his own). In its place both substitute a kind of living in which meaning is the meaning of the life lived. One way of seeing it is to see how the particulars of one's life become then very relevant. Kierkegaard referred to this as "finitude" sometimes.
BTW if you are interested in this you might check out "The Jargon of Authenticity" by Theodor Adorno. I don't really agree much with him but he lands some very stinging blows on those who carry out philosophy from the bleachers and make authenticity - a kind of cultural result of existentialism - mere jargon. Its sort of the same argument once removed.