I love this post. Possibly my favorite thing about Wrath of Khan is that Khan has a fairly legitimate beef with Kirk, so it's not exactly a case of good vs evil.
I love how Khan also acted as one big fuck you to Kirk. It really embraced his character as a flawed hero. Took his arrogance and huge ego he had and belief he could get out of any jam and let it it all come back to bite him in the ass and cause his world to crumble around him.
Nicholas Meyer basically took the percieved faults of Shatner himself as a person and merged them with the Kirk character to turn the character from a Buck Rogers like super hero from TOS + TMP into an actual real human being. It was brilliantly done.
Here's another thing about Wrath of Khan.
The "wrath" part of the title, meaning the Reliant shooting up the Enterprise and becoming a submarine movie in space is the B plot.
The A plot in Wrath of Khan is a human story of ageing, and responding to the consequences of growing older. As in: getting a job, getting married, having kids, retiring gracefully, and then dying.
Kirk rejects all of this. He still sees himself as a swashbuckling hero that can never fail, with the command of a mighty starship and a girl in every port.
Khan didn't reject this. He had a home, a wife, and I believe that Joachim was his son (either biological, fostered or groomed to be an heir). He was set for life on his new world of Ceti Alpha 5.
Kirk struggled to retire. His ship was taken from him and he wants it back.
Khan couldn't retire. His home was destroyed, no help arrived, and he wants revenge.
Kirk embraced his son as his own late into the movie and used it as extra motivation to survive. Khan saw his son die and it resolved his will to kill Kirk by any means necessary.
Spock's death sealed the whole death part. And in doing so, brought about literal new life, and Kirk essentially rejecting his fate again - as he now feels young again.
This is combined with the whole meta commentary on this being the latest incarnation - and possibly the death of - the Star Trek franchise. It had followed this path from the series, to the movie, and now it was old too. And just like with Kirk, it felt young again.
It's late where I am so my brain's a bit fuzzy. Hopefully you can see what I mean. There's the other elements with Scotty's nephew and stuff that feeds into this human story. But generally it's a great movie on so many levels.
I feel that The Undiscovered Country is a slightly better film, as it provided complete and utter closure for both the Original Series and the era in which that series was inspired by.