For some reason I suspect Picard would have found a way to save the Ocampa AND get home right away.
I highly doubt that. The only possibility would be to 'ensure' that the Array be destroyed right after it sends Voyager home, but since Voyager would then be home there would be absolutely no way to ever know for sure if the Array were actually destroyed as intended.
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Regarding the question in general, I would say DS9 is the easiest to answer: Neither Picard nor Janeway would do half as well in Sisko's position as he did. The first major obstacle is, of course, the Emissary. If Picard and Janeway aren't the Emissary, then a huge portion of DS9 is undone, including much of the cultural exchange that brought Bajor closer to the Federation (DS9's original mission) and one of the most pivotal moments of the Dominion War (DS9's later mission). Even if we rewrote their characters to say that they actually were the Emissary, neither one of them would ever really accept that position and thus would still never achieve the same level of relations with the Bajorans or the Prophets.
I also doubt if Picard would truly understand the importance of the civilian life on the station or the continuity of that civilian life even between different regimes. Under Picard, Quark would've been gone from the first episode and most other civilians with him. DS9 would've been almost exclusively a Starfleet/Bajoran Militia station guarding the wormhole but not really attracting any sort of cultural exchange. I'm not sure where Janeway would fall on this question, but I'm guessing maybe closer to Sisko than Picard.
The other big elephant in the room is the Dominion War itself - Picard would be more diplomatic to start with. Maybe he might even wind up negotiating a peace treaty of some sort at the outset, and he certainly wouldn't mine the wormhole as a pre-emptive defense measure. But his very successes would be the literal death of the Federation. The Dominion is obsessed with control and is shown to betray and overthrow even those with whom they make treaties. The Dominion also was nearly able to destroy the Federation and Klingons both using just the Cardassian fleet and the small number of Dominion ships that made it through the wormhole plus whatever they could build and crew from within the AQ. If that tactical separation between alpha and gamma quadrant had not been in place, the Dominion would've steamrolled over everyone and proven themselves more unstoppable than the Borg (since, unlike the Borg, the Dominion actually uses fleets). That is, if they even allowed any of it to go a 'Dominion War' scenario at all, rather than using infiltrators to start an 'Alpha Quadrant war' wherein all the AQ powers just tear each other to shreds, leaving the Dominion to mop up, or rather than simply replacing all the political leaders and effectively 'signing treaties' with themselves until all political power rest de facto with the Founders.
Where Janeway would fall in the DW question is a weird one to answer. Based on what we've seen of her, I would say she would make similar choices to Sisko, though she would not have the advantage of being tight with the Prophets. But everything we know about her in her capacity as a leader is based on her behavior in an extremely unrepresentative situation. If she at times seemed severely cautious, maybe even paranoid, in the face of alien cultures that were anything less than open, well, she actually had really good reason to be. She was alone and carried the sole responsibility for her people's safety and happiness and she actually was beset on all sides by dangerous, malevolent races. What would Captain Kathryn Janeway even be like if she had never experienced her trek through the DQ? I honestly have no idea. (For the same reason, I will say off the bat that I really have no idea how Janeway would work out in TNG, either).
So DS9 had to be Sisko.
Voyager, I would say could not have been Sisko. For one thing, at the start of his story he's lost all hope and faith in Starfleet. He's on the verge on leaving altogether. He's helped through it by the Prophets, but without them, he was keeping himself stuck in that moment eternally. If, during that time, he were flung to the far side of the universe, would he even still want to be Captain after that at all? I honestly doubt it. Captain Sisko probably would've stepped down and just focused on being a father to Jake, unless something absolutely forced him not to - and that obviously wouldn't be a good situation for anyone, since a Captain whose heart isn't in it is disastrous. That's without even going into his major issues with the Borg. Most definitely, Sisko would never have been able to ally with them even temporarily, and he almost certainly wouldn't have rescued Seven of Nine.
Regarding Sisko on TNG, I again have to say there's no real way to answer that. If you take Sisko back to before Wolf 359 you are erasing the most fundamental layers of his character, so there's no telling what he'd be like.
So that leaves Picard on Voyager. As I said, I don't believe for a second he would've been able to just magically fix everything. I do think this is probably the most likely crossover to actually work as Picard's diplomacy could have perhaps made some situations easier and he can be a disciplinarian when he wants to, as well. His Borg issue, unlike Sisko's, is not at the center of his character and if Picard were placed in command of the Voyager instead of the Enterprise, he would simply never have had the Borg issue, until he met them in the Delta Quadrant. Even then, his TNG arc showed him capable of overcoming it anway.
My biggest concern with Picard on Voy is that he's too by the book and inflexible. I suspect he would allow himself to be talked into accepting the Maquis as shipmates rather than prisoners, because there really is no other practical option. But I kind of doubt whether he would ever really treat them equally with his own officers, because they are literally criminals. Terrorists, even. I think that may be going to far for him, and as a result, I question whether Voyager would ever truly become a coherent, reliable gestalt.
