No contest. First Contact.
When it comes to a story about our main character seeking revenge against the bad guy, Picard's is the way better story. We see a Captain who once gloated, bragged and preached about how awesome and godlike humanity has become over the years be reduced to an irresponsible leader in a crises with the whole galaxy at stake. He uses his rank and authority to force his crew into a suicidal struggle against an enemy that steals your very soul. And the one person who talks him out of it? A woman from the 21st century who lives in a rusted, torn up Montana town. You remember how the crew used to say about humanity from the 21st century? Like how there was little to nothing that redeems them and that it was a wonder how humanity survived at all? Yep. One just helped save the day.
What do we get with Kirk? Revenge is bad, but trying to beat the living snot out of a person who had already surrendered out of revenge is good!
At least First Contact didn't have magic blood.
The problem I had with Picard's actions in FC:
If they hadn't already essentially covered that aspect of Picard's reaction to encountering the Borg again in the TNG episode "I Borg" (where he breaks down and instead of destroying the enemy that violated him - he treated it medically and fed it, then gave it a name, and sent it 'home'); and the follow up story about that same Borg in "Descent".)
While FC is indeed the best (and IMO the only marginally watchable) TNG feature film (to this day I still find any scene with Data and the Borg Queen cringeworthy as even two good actors couldn't do much with that mess); in comparison with STiD, FC comes across as a big budget TNG 2 part TV episode (even down to the ridiculous A/B storylines in one episode aspect, which I hated in TNG.)
STiD blows away FC in every aspect. It really does recapture the essence of the Kirk and Spock characters, shows their friendship progressing, and you get the sense they both grew as characters.
Contrast that with FC where Picard basically turns into a raving action figure; and when Worf shows up on the Bridge after effectively loosing the Defiant (and probably a fair number of crewmen were killed) - the first thing said by Riker to Worf (after the offhand "tough little ship")is: "You do remember how to fire phasers?"
yep, stellar character interaction there.