I sort of agree, but if you look hard enough, you can find parallels in most of the movies. A star or planet explodes or is crucial to the plot in TSFS, VOY, TUC, GEN, and ST09.
Picard is arguably out of TNG series character in ALL the TNG movies.
INS-influenced by fountain of youth
NEM-compromised by twin (despite statements to contrary)
Interesting thought on Picard there. His darker "movie personality" is interesting. As you said, they do go to the trouble to explain it in each of those movies, so it was on their minds when making the film.
Into Darkness is the better film. First Contact felt like two separate stories stitched together. Picard was completely out of character and they destroyed the Borg.
I watched the FC extras yesterday on the blu ray, and the piece on "The story" really showed to me that they did put a lot of work and thought into their choices, foreshadowing, integration of the plots.
Into Darkness feels a lot more like each scene is trying to reference something classic, but not bring anything to the table for the plot on its own, and then it's loosely strung together. While the pacing of the movie might be faster, when you actually get into it FC had a lot more to offer on the writing end.
On the pacing note, I think the pacing in general in action movies these days is getting to be a bit much, it has to be so epic and explodey that there's no time to breathe and actually feel something for the characters. There's not much to feel for any of the characters outside of Kirk/Spock at all in the new movies. The back up crew are mostly caricatures of the prior versions. That said, I didn't hate Into Darkness, don't want it to be about that. It was fun for the most part. Don't know that I'd really re-watch it, not a lot of depth.
FC allowed that pacing for action and feeling. We felt that Picard was over the edge, even though he was mostly right. We felt the fear of Lily. Zephram Cochrane was probably the best part of the movie, feeling his discomfort from the hero worship. It gave us time in between the action to reflect, which I think is important. Troi and Riker offered comic relief in a lot of instances. And I think if all we had of TNG was this movie, there's enough there to care about the characters.
Into Darkness, by contrast, if that was all you'd ever seen or heard of Kirk, Spock and company, can you say you'd truly care about them? And why if that's the case?