First, in the speeches alone there's a sort of feeling that not only make those characters great and those particular episodes fantastic, but actually, I think, really highlight the difference in mood and outlook each stance has.
Picard's speech comes in an episode that has a ton of philosophical questions--not the least of which is the title question, what IS the measure of a man, ie, what defines us as living creatures and what are our rights, as such--but is also delivered in a manner that, while definitely sharp in tone, really exhibits a sense of idealism.
Which is what Picard as a character is--an idealist. As a captain on the show he's a lot like a college professor or a 19th century naval officer who's "well-bred and well-fed," and so Picard as a character, usually, takes to defending the rosier of options, he's a diplomat and a thinker, he actually IS the kind of person who would read philosophy and classical literature avidly--he actually keeps a copy of Shakespeare on his desk from which he'll quote from occaisionally...but with my inner dork showing, I digress--and I feel that this is somewhat comparable to the typical view and stance of those who would side with Picard and say that ends are NOT justified by means.
Picard's idealism allows him to see a picture of man as being essentially GOOD, very Locke-like, and that, in keeping with Locke, each person has "natural rights" which cannot be trampled upon by ANYONE, hence his reason for defending Data when the alternative--take Data part and create a slave-race of Datas some time in the future--could benefit the greater number...
For Picard, Locke, and those like them (on the whole, if you disagree or feel I'm unfairly lumping you in here, I apologize and don't hesitate setting me straight) GENERALLY the "greater good" does not apply OR, if it does, it can only apply AFTER those "natural rights" do. Picard certainly does act for "the greater good" many times throughout the show, but almost without exception he does so ONLY when this either doesn't conflict or conflict seriously with natural rights or when the situation is so dire and immediate that it can be argued that ethics don't apply.
Sisko, in contrast, is the polar opposite of Picard, in his tone and temperment and views and everything--they even have the two meet in the first episode of Sisko's show and the latter shows just how much he despises the former, and the former how irresponsible he sees the latter as being.
Sisko is anything BUT an idealist. He loses his wife (and lost her fighting the Borg while Picard was forced to work for them against his will, hence his hatred for Picard and blaming him somewhat for her death), he has to deal with crooks and cutthroats all day, for half of the show he's not only embroiled in a war but the leader of it on the front lines, a sort of Patton-in-space...that doesn't leave a lot of room for idealism and philosophical contemplation, let alone that Shakespeare Picard loves to quote.
As a result, just as Picard's speech is given sharply but with a distinct air of idealism, touching on a lot of philosophical and theoretical ideas, Sisko's is far more rough and focused solely on the action and its consequences--outright he says he lied and cheated...but that because of the potential consequences, namely getting help in that war from the Romulan people by essentially lying to them and allowing the deaths of a couple of men to aid that cause, he can live with doing this wrong, that it's justified, if not MORALLY, then PRACTICALLY.
I LOVE both speeches, both episodes, and both captains (and Kirk as well, of course, Kirk, Picard, and Sisko are great captains and characters) and I will admit that within the context of each episode I agree with both speeches and both men--Picard's argument, while idealistic and lofty, is made in a setting where that's called for, and Sisko's Machiavellian dealins are done in a situation where it may be the only way to win a bloody war.
But on the larger question of ends vs. means...
Sisko treats everyone equally, as just one more piece to get the result he needs--which I DON'T agree with philosophically; again, I hold people are individuals and must be treated as such, and so we cannot just assume that "the greater good" IS, in fact, the greater choice. Suppose to save 100 people you had to murder one person--and that person, you very well know, is Shakespeare or Mozart or Einstein or whatever great figure you will. Mozart IS worth more than 100 junkies or murders or, as controversial as this may sound, even "regular" people.
1 Mozart > 100 obiwanobiwans. ;)
The consequence of this thinking, however, is that if there IS a qualitative difference in people--and it's NOT inherrent or in the blood or genetic, I'm not talking about any racial superiority, THAT'S nonsense, I mean a gained qualititative difference, ie, molding oneself into the greatest composer of all-time--and these qualities are forever being acquired, adn thus people changing, then I'd submit there is no real "end" bot rather just means after means, people constant acting upon people.
I cannot see, ethically, the rationale behind killing a few to save many on the surface of it, as those few, while fewer in numbeer, might be greater in intelligence or mastery or genius or what have you. Picard is right, in my view, both times--we should certainly apply justice and extend rights equally--or as equally as logic dictates--but we cannot treat all beings the same, and so we cannot treat the metallic Data as we would most metallic objects, AS objects, but must treat him as a person.
Ironically enough, equality leads to inequality if this is not done--if all are treated equally then blanket judgments are made and the nuances of people are lost, and so they are treated unfairly and unequally in relation to their general quality of life.