Leliana is the only option that has any real chance of bringing peace and stability to Thedas.
I do NOT trust Vivienne. My interpretation of her character was that she opposed the Circles breaking away from the Chantry not because she truly believed in the Chantry, but because she'd lose her power and prestige as First Enchanter and court Mage to the Empress. She's not so much a Chantry Loyalist as someone who sees the Chantry as a path to her own personal power. That is ALL Vivienne truly cares about. She lived her life in the lap of luxury, with no experience or concern about the abuses that OTHER Mages in Thedas were suffering through. She wants power and authority, and has no concern for those who are hurt as a result. As Divine, she basically returns things to the way they were previously, recreates the same system that led to the rebellion and war. Most Mages are NOT going to return to the Circles, and even if she manages peace for a time, ultimately the same excesses and abuses on part of the Chantry and the Templars WILL become inevitable, and Thedas WILL be right back to war. The chances of the war restarting before Vivienne dies is pretty close to 100%. Honestly, in my opinion, Vivienne is worse than Corypheus. As bad as he is, at least he is motivated by some twisted belief that the world would be a better place with him as a god. Vivienne only wants power for her OWN benefit.
Cassandra is a better choice than Vivienne, but still has problems. Cassandra means well, but her reforms will ultimately be a stopgap. Templars or no, Mages are NOT going to return to the Circle system in large numbers, and they will not agree to be under Chantry oversight for long. Peace may last for longer due to Cassandra's reforms, but the abuse will inevitably happen again, and war between the Mages and the Chantry will ultimately return to Thedas, just as with Vivienne. maybe just not as soon. While her time as Divine will likely be relatively peaceful, there is nothing to stop Cassandra's successor, or some future Divine, from undoing her reforms, and restoring the same oppressive system that led to the Mage/Templar war in the first place.
Leliana ends the Circle system and disbands the Templars. While that may not seem the best option, it's the only one that will promise any true peace. The Chantry's actions have shown that it can NOT be trusted to properly police and protect Mages, that it will WILL eventually abuse it's power. The Mages are not going to tolerate that abuse. Allowing that same repressive system to return will just be doing it all over again. To have a chance at peace, Mages MUST be outside of Chantry authority. Period. Leliana's extensive reforms, and the alliance of the Mages and the Chantry with the Inquisition, allows for stability, as each group can serve as a check on the excesses of the others. The New Seekers of Truth can help to prevent the rise of Maleficars, the Inquisition can stop the Chantry from becoming too powerful again, preventing their excesses, and the Mages could serve to police the Inquisition and keep THEM from getting abusive and repressive. These reforms are the only chance there is at preventing the war from restarting, and the only chance at any real long term peace. While the possibility remains that the conflict will restart under Leliana anyway, it is still just a possibility, as opposed to the absolute certainty that will result from Vivienne's appointment as Divine.
Leliana is a gentle person who often sees the best in everyone. She also has the instincts to know when to use a firm hand. She understands that there is a time and place for force, and will not use it unless it's absolutely necessary. She's a good hearted and idealistic person, but one who nonetheless is pragmatic when she needs to be. And that makes her the best choice to prevent a war.