This is a VERY tough choice.
On the one hand, INTO DARKNESS was atrocious, had a story and script with more holes in it than swiss cheese, and was a horrible retreading of TWOK.
On the other hand, SECTION 31 was atrocious, had a story and script that was terrible, and was a waste of Michelle Yeoh.
I look at these two in the same way as two episodes of ENT: "PRECIOUS CARGO" and "THESE ARE THE VOYAGES...". While I think "PRECIOUS CARGO" is absolutely the WORST episode of that series (to this day, I still cannot find one thing about it I can defend or find redeeming), I despise the finale far more.
I consider SECTION 31 to be the worst movie in the franchise... but I hate INTO DARKNESS more, so I will, reluctantly, cast my final vote for SECTION 31.
Why? Because the Enterprise is a STARSHIP, not the seaQuest. It was a bad start to a bad movie, and I just CANNOT get past the stupidity of that sequece.
Plus, at least SECTION 31 tried to give us something new about the Lost Era, like a younger Rachel Garrett, who despite the bad dialogue ("Chaos is my friend with benefits" is one of the most cringeworthy pieces of dialogue the franchise has ever given us), was not a bad character.
STAR TREK INTO DARKNESS - 0
STAR TREK: SECTION 31 - 1