I don't think they're the same movie. I do, however, think that by including Khan, by making an issue of the call backs, and by having Spock sub 1 ask Spock Prime about Khan and having Spock explain him in such ominous terms, the movie itself invites the comparison.
Others have said that including Khan was the big mistake; I agree, but not in the way that I think they meant. Including Khan (and everything related to TWOK) was a big mistake because it's pretty much screaming to the audience "If you thought TWOK was good, take a look at what we have here!" A friend of mine talks about the contrast effect a lot, the difference between expectations and reality, and how it affects and colors our experiences. By inviting comparison between STID and TWOK, they're almost guaranteeing failure.
What they have is a perfectly serviceable action movie, but it never achieves the depth of TWOK.
There are a lot of things I enjoyed about STID. First it addresses some of the frequent criticisms I saw of Star Trek (2009), particularly the rapid fire promotions. And some of the set design issues. And JJ Abrams exercised a bit more restraint on the lens flares (as much as I enjoyed Star Trek [2009] the lens flares were way over the top and frankly that with the documentary style camera work I left with a serious headache). He was much more judicious here. STID looked like more professional. I also loved the Section 31 angle and Admiral Marcus (who reminded me a bit of his 'alter ego' on Enterprise who was equally good).
But the whole Khan angle really pulled me out of the story. And a shame too because Cumberbatch did an otherwise good job--I really wish he was 'John Harrison'. But by bringing in Khan to the movie, fair or not, it was going to inevitably be compared to TWOK--for many fans the high water mark of the movies. Now no matter what they did it was going to be compared to TWOK. It's not a remake, other than a few lifted scenes. That is true. But comparisons don't just occur between remakes. Comparisons are frequently made between sequels and movies that reuse the same character, even in different stories. So I actually don't think it's unfair personally to compare it to TWOK.
And the melodramatic scene when he reveals his true self--"My name is ....Khan" did elicit an eye roll from me. My first reaction was "I knew it" because the more Bob Orci and co. denied it was Khan the more I believe it was going to be Khan. And just disbelief. I couldn't believe they actually went and did it.
And yes, the reactor scene, then Spock yelling "Khan" caused another eye roll for me. It looked like a blatant attempt by TWOK fans to be cute to me. "Oooh, let's redo the final scene from TWOK, but reverse the characters and have Spock scream Khan instead.....that would be so COOOOL!"--but it wasn't, IMHO.
In fact, the scene cuts away so fast to the
Vengeance roaring into the atmosphere just as Spock screams it that I always wondered if Abrams himself thought it was a bit over the top and he just wanted to cut away to the next scene ASAP.
And don't even get me started with the magic blood thing. WTF was that? Seriously? It was like they knew they couldn't
really kill Captain Kirk and they hit a mind block and someone blurted out "MAGIC BLOOD, Khan has magic blood".
But there are other things I liked. Leave Cumberbatch as John Harrison, rework the Kirk death scene and find a better way to resurrect him (or I suppose if there was no Khan then maybe magic blood could still work--a bit dopey but at least it wasn't some characteristic the character never had before since it'd be a new character). Then the rest of the film works pretty well I think.