As my main character, I chose to save Amaranthine. As the Queen of Ferelden as well as a Grey Warden, it was her duty to protect the people and save the city. She couldn't allow it to burn, as she would have lost a valuable trade route and source of income for Ferelden as well as a well forged alliance between the city and the Grey Wardens. Whether she would die at Amaranthine was besides the point - she had faced more dangerous odds in defeating the Arch Demon and had survived when she shouldn't have. And staying to defend Vigils Keep was not necessarily guaranteeing her safety either. It was a tough decision, but it had to be made to secure Ferelden's foothold in the area.
Vigil's Keep was a watch post for Darkspawn and was created to protect the area. After bringing in a Dwarven stone smith to fortify the walls, plugging up any way that the Darkspawn could have made it into the keep, as well as having amazing armor crafters that she had worked with in the past to ensure my Grey Wardens were well armed and well armored, she left them and her companions to hold the walls until she could return to them and help them in their fight. Anders was left behind because he was a semi-reliable healer and would tend to the wounded. Justice was left behind as a valuable front-line fighter. And finally, Nathaniel was left behind because I knew he would be a valuable archer at the top of the walls.
Unfortunately, she was unable to return to Vigil's Keep because she was presented with the opportunity to slay the Darkspawn's leader, their General, in a sense, the Mother. In that decision, it was either return to the Keep to help her Grey Wardens or strike a crippling blow to the armies that threatened both Amaranthine and Vigil's Keep.
Ultimately, she managed to save both the city of Amaranthine and Vigil's Keep, keeping a valuable city from falling, ensuring the continuation of a city with great opportunites as well as keeping a foothold for the Grey Warden's in future fights. However, she is faced with the loss and disappearance of some of her companions. Anders has completely disappeared, but she is aware that he is prone to running away from his problems. Justice's body was found beheaded by Darkspawn and his corpse was rightfully returned to his wife for her to mourn his loss. Nathaniel survives and goes on to save her brother, in which he is reinstated his lands, then continues his journey as a Grey Warden.
While she is saddened and mourns the loss of her fallen and lost companions, she believes that she made the right choice in leaving the protection of the Keep in their very capable hands.
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Now, down to the nitty gritty... Even if you manage to save both Vigil's Keep and Amaranthine, the game is bugged and doesn't register this event. Any companions left behind at Vigil's Keep "die" when they are not supposed to. When transferring your game to DAII, it will register that Nathaniel (if left at the Keep) is dead and will not appear in your DAII game. The only way to "save" him, is to take him with you to protect Amaranthine.
Luckily, the Dragon Age Keep has fixed this bug when transferring to DA:I by allowing you to pick the option of saving both the Keep and Amaranthine, and still keeping Nathaniel alive while doing so. Unfortunately, the Keep will not transfer this option into DAII, so make sure you take Nathaniel with you to the Mother fight if you wish for him to survive.