Rei; the first children

Actual one-on-one contact between these two is very limited; just about twice, and both with a different Rei. What ties these two very different, yet similar, people are their origins—Shinji first makes this connection when he meets Kaworu. They are both born from the same matter, but have grown in largely different environments. While Kaworu spent most of his entire life held within an artificial womb by SEELE, Rei was raised like an almost adopted child by Ikari Gendou, Shinji's father. Kaworu had never received any form of human affection from his guardians, he knew his purpose: to carry out SEELE's will. Rei, on the other hand, was effectively loved by Gendou, though mostly because she embodied his deceased wife, Yui. Though like Kaworu, to some extent, she knew what she was meant for.

No. We're not the same. We might be very similar, but we are not the same. Ayanami Rei, Stage 62

Even though they both came from unnatural means and could have bonded through that, Rei did not like Kaworu. His depth of knowledge regarding her frightened Rei, and she could not agree with his casual demeanor. Rei also recognized they served different people, for different reasons, and for different goals.

From their brief acquaintanceship, Kaworu did acknowledge her skill as the pilot of Evangelion Unit-00, though he did it in an unflattering manner (he tells her, "I saw you throw the spear. I thought you'd be a somewhat heftier girl."). When Rei II self-destructed Unit-00 in order to save Shinji from Armisael, Kaworu showed no sympathy towards her, stating that she was foolish. To Kaworu, a sense of self and one's own existence is highly important, so he viewed her sacrifice as wasteful. It's clear from Kaworu's final words in Stage 73 of the manga that he considered death to be the ultimate choice when no alternatives exist—not something idly done.

But our difference lies in whom we have met, and how we have lived thus far. Nagisa Kaworu, Stage 71

After Rei III is brought out to replaced the deceased Rei II, Kaworu meets her again. This time, however, it is Rei who voices their similarity. Amused, Kaworu describes their physical similarities, but also points out their differences. He quotes her previous rebuttal about the two of them being the same, and mocks her for the missing memory he knew she could not possess.

I think at this point, Kaworu recognized how much of a doll she was, much like the way he was. If he could spare any pity for her at this point, he probably would have felt sorry for her. Both of them were replaceable, and both were being used. Right before his death, Kaworu sees Rei standing above himself and Unit-01 in Central Dogma, and they share a last glace devoid of any real feelings.