What integrity did Kirk have in A taste of Armageddon/ A private little war or did Picard have with I Borg or Penpals or Admiral Satie in The Drumhead?
Kirk had a
shit-ton of integrity in both those instances. In bot cases, he tried to right a horrible wrong. In "Armageddon" he was to save his own crew, and the planet(s) with them. Hell, he was using cold-war tactics (mutually assured destruction), but in order so
save people. And in "private war" his goal was to "correct" the klingon incursion, to bring the people back to their original ways, and away from the opression of the klingon-backed warmongers.
But the most important difference is:
Both of these instances were HEAVLY debated.
There was much discussion going on. Testing out limits. And different opinions being voiced about the way how to proceed and if it was justified. You might disagree with the
conclusions Kirk came to (as I disagree with many of Sisko's conclusions), but the reason you remember it so well was because of how many thoughts went into it.
Compare that do Lorca leaving Mudd behind
just 'cause. There was no reason, no debate, no moral conflict, no
anything. Lorca was just being a dick. Leaving another being back for certain torture and death. Not because it would improve ehir own chances, or because he could only save two people. No. Just because he
might have cooperated with the klingons (to, again, evade
torture and death). That's just immoral, however you want to spin it.