In all honesty, Mary won; Mary mothered the future Earl and saved the estate. Edith can't leave anything to Marigold because she's illegitimate and can't admit Marigold is hers until the 1980s as it was stigmatised before then and by the 1980s Edith would be in her 90s or already dead.
Wrong, even by being Bertie´s daughter, Marigold would never inherited Brancaster estate, those estates always were inherited by the first born son, other childs that they could have would inherite far less. Edith said that she is working in the magazine so one day Marigold could have it.
Edith married a Marquess a higher tittle than a earl, in england there are 35 app, compare to 250 app earls. Even more, he married a rich marquess (Brancaster is by far more bigger and lavished than Downton, even Robert and Cora were amazed by the place, and even Rose told that the papers in NY were speaking about them). In the end Edith outranks all in their family, she is now a marchioness, higher than Cora (a countess), her grandmother (dowager countess), Robert (a earl), Rose (the wife of the future lord sinderby), Isobel (now Lady Merton), Rosamound (earl daughter), Mary (earl daughter). The only tittle that Mary has is by being an earl daugther. Plus, outranking all of them, she is now rich by marrying Bertie (Rose spoke about how the papers in NY were writting about Lady Edith and her millionaire marquess, we are talking 100 years millions dollars), and even more, Edith has her own publishing company.
Mary, has her share in the estate, who is tied to Downton, so when dies, her share came back to the estate and it will belong to George. Plus, Henry is only opening her car business, and they only are selling used cars.
In the economic aspec, Edith ended far better than Mary, there is no doubt about it.
But in the end it wasnt a competition, even the characters didnt show any sign abou it. It was about accepting that their relation it would never be great but at least would be civilized. But it was Edith who was the mature in the relation in the last period, when Mary broke up with Talbot she started to making all there miserable and even sabotaged Edith´s relation; when Edith broke up with Bertie, picked herself and went to work and didnt cause any troubles to anybody and had the courtesy to came back and congratulate Mary. Only in the last moment Mary finally decided to no continuing behaving like a spoiled brat.