What it does is make the show a lot more realistic. You just can't be involved in politics and war and always remained morally unblemished. It is naive to think otherwise. There are times when you have to weigh what is more important and whether it is worth it. He got it off his chest, weighed it all in, and concluded - can I live with being accessory to murder if it changes the course of the war and ends up saving the Quadrant and millions of lives? Was it worth it? And he concluded it was and he could live with himself. You may not like his conclusion, but it felt real.
I posted this in the DS9 forum but I'll repost it here. It represents my views on this "The world is grey" stuff we keep hearing:
"As for this "there's no such thing as black and white" stuff, I have to humbly disagree. I know it's a bitter pill to swallow but there really ARE monstrous people out there who really are just bad to the core, and there are people out there who are capable of genuine kindness and compassion despite being in a bad situation. Frankly, whenever I hear how it's "immature" or "silly" to think that the world is only grey I can only think that it's just as immature or silly to refuse that there could be black and white in the world. It almost comes off as cowardly, to refuse to accept that maybe there are very bad people out there or that there's such a thing as a good person, because it can be used to ignore situations thinking "Well, the world isn't black and white so it's best not to get involved" or "there's two sides to this so we better think out everything" when it's obvious who's good and bad."
And Sisko's talk at the end sounded more like a guy who was trying to convince himself more than anything else. That he had to make a log to convince himself (and didn't do a good job from how he talked at the end) is the actions of a man who isn't, and likely will never, be totally convinced of his actions.
As for Picard, "Yesterday's Enterprise" showed he could weigh major decision affecting reality itself if need be so no worries about his character.
I agree that there is whitish, blackish and grey. White and black....nobody's completely a saint, and nobody's completely a devil.

A great criminal is capable of some good deeds (Dukat) and a saint is capable of horrific acts (Kai).
The point here is that it's a matter of perspective. It is sometimes not "obvious" who is "good" and "bad". Klingons in TOS were not "bad". They just happened to be antagonistic to the Federation. Romulans in TNG aren't "bad". They just happen to be antagonistic to the Federation.
I respectfully disagree with your view on Sisko. He was not trying to convince himself. I'm sorry you see it that way. No worries on Sisko's character either.
As for Picard, I did not say that he could not make or contemplate such weighty decisions. My point and opinion is that his belief in the laws and values of the Federation and Starfleet would not permit him to be an accessory to murder and yet continue as a Starfleet officer. If Picard had been in Sisko's position, he might well have resigned after the incident.
"Yesterday's Enterprise" was a no-brainer once Picard came to accept Guinan's intuition. It is clear that sending the Enterprise-C back to its
original timeline so that 40 billion lives (lost in the war with the Klingons) could be saved and the timeline restored
was the right thing to do. However, it is not so clear that deceiving the Romulans into joining the war against the Dominion by having one of their ambassadors murdered was the right thing to do.
I would also have you know that I consider Picard to be the best character/captain/leader in Trek.
EDIT: * BOOK SPOILER ALERT * As an interesting aside, if we were to consider events in the Star Trek universe after Nemesis as portrayed in the books (which is non-canon but yet official), the devastation wreaked by the Borg invasion in the
Destiny series causes Picard (on spl. orders from Starfleet) to order Geordi to prepare the Enterprise-E to fire a thelaron weapon to give them a fighting chance against the Borg. Geordi to his credit, refuses to comply citing the moral depravity of using the weapon against
any lifeform and threatens to resign. Picard subsequently capitulates having realized his error in moral judgement and events unfold differently.