While everyone can point to a few things between them (Uhura Prime's song in Charlie X), she also kissed Kirk Prime and seemed to have some understanding with Scotty.
NuSpock is NOT Spock Prime. NuSpock lost his mother much younger than Spock Prime, lost his planet (which did not
happen to Spock Prime), was told by Spock Prime to live his own life (which Spock Prime realized decades
later), and met nuUhura at a different/much earlier point in his life--and her life (evidently, since she was still a cadet instead of an established lieutenant).
It's implied--and pretty much stated in this movie--that Spock Prime is not
telling nuSpock all that much, recognizing that the timelines are different so choices will be different. I mean, Spock Prime met Khan while already friends with Kirk, what, almost 10 years later in their lives. And re-met Khan MUCH later in their lives, after
his friendship with Kirk was long-established by decades, decades more than nuKirk has been alive.
I am SO enjoying discussing these characters, and some of the relationship between the timelines.