THIS is TOUGH!
my two favorite ST movies (nick meyers was the best thing to ever happen to Star Trek, I maintain).
I love where Khan went as a character. I love the sacrifice of spock (nevermind ST3, blech). I like that a lot of the characters started to feel old, even if they weren't quite there yet. Worn out would probably be a better term. I love how the end was a bit of a rebirth for Kirk "Young, I feel Young!". and who can forget the battle of the Mutara Nebula.
ST6, the characters weren't only feeling old, but they were actually old. Dignified, still, but old. I like that this film really hit home with the political ramifications of the crew's actions. It felt like the-larger-than-the-crew was at its largest. The humor wasn't over done, and added to the movie instead of distracted you from it: "1 day, 1 night, *skick* kobayiashi maru." But I feel like Kirk evolved as a character more in this film than in Wrath of Khan. Hate to faith is a bigger transformation than Feeling old to feeling young.
From a design and asthetic standpoint, neverminding that they were made a decade apart, I actually feel like that the biggest difference is in the design of the bridge set. In that biggest difference ST6 wins, hands down. As far as the rest of the sets? ST6 still wins: Compare the Regula station to the Qonos One's interior, for example.
From a perspective of impact of mythos. Personally, for my own version of Star Trek (cut out the useless fat!) - ST6 made a greater impact there, too.
It's very very close, but I gotta give it to ST6.