I've had this conversation before with some friends. I felt the last movie did well to capture the essence of the cast of major characters from the original series, and that the movie (mostly the ending) wasn't in spirit of Star Trek*. The antagonistic force wasn't either (though that's fairly common even in the past movies) and he wasn't actually terribly interesting.
I have high doubts that this new movie will be any different in its "non-Trek" spirit, and will not go out of my way to see it unless I hear otherwise. I hope to be proven wrong.
*By "spirit of Star Trek" in this case, I mean a setting where a) the future is generally optimistic and, at the very least, humanity has mostly overcome things like greed and vengeance (and when someone doesn't, the narrative makes it clear that they're failing) and b) the narratives often address some social commentary and/or ethical dilemmas. I think Star Trek: The Undiscovered County probably captured this the best out of the movies. Even the generally most well-received Star Trek movie (First Contact) had a "B plot" that showed a new dawn for humanity and a moral dilemma in the "A plot" (Picard going Capt. Ahab). The past Star Trek, on the other hand, was generally just an action movie, and even said "vengeance is OK" when Kirk and Spock decided to fire on Nero after he was already going to die for certain.
On a very nerd-related tangent, while I actually thought the 'premise' of the reboot was fitting and done well enough, a friend pointed out that the whole "destruction of Vulcan" thing should have flagged the attention of the future Starfleet who goes out of their way to travel back in the past to fix any huge time travel issues like this one. I never really got how Star Trek could keep doing time travel once they established that parallel universes existed... oh well.
EDIT: To be clear, I think this past Star Trek movie was entertaining, and won't avoid seeing the new movie if someone drags me along after hearing reviews that it's at least as entertaining as the past one.
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