My family and I have been blessed to know Gerontissa Aemeliani and the other nuns for about fifteen years now...I have also been spiritually blessed to have met Geronta Dionysios. I know the nuns from the U.S. and also from Greece. They are selfless servants and friends to so many who know them. During my years spent in Greece, they were highly regarded by the expat community of Americans who visited them (many were not even Orthodox, and many who were, were not even particularly observant or religious) and of the local inhabitants who resided near their monasteries and fondly called them the 'foreign nuns'! 
Why would these expat Greeks hold a monastery in a higher regard than a village church, a village Priest?
Monasticism has always been the bulwark of the Orthodox faith. The monasteries have produced almost all the saints and theologians in the Church, and with some exceptions, most of the monastics have proven themselves by their works and sacrifices that they are true people of God. In contrast, many priests in the Orthodox Church have entered the priesthood merely as an occupation and not because they had a calling from God. This does not mean that many of them are not holy, and there have been priests that did become saints, but it is a much more rare phenomenom.
Anyway just so I won't be slandered by those on this forum who have a propensity to do things of that sort, what I stated is what I heard from Greek priests themselves. Also you have to realize that Abess Amiliani and the foreign nuns, (some are German as well as Americans), helped to restore some Greek monasteries and also helped to establish a few new ones, while in contrast most Greek priests are not even educated. It was never part of the Orthodox Church to educate priests the way the RCC did, but rather to choose some child in the village, probably one with an exceptional voice, and train them for the priesthood in order to serve the community.
Because many of these priests considered it merely an occupation, they never acquired the respect from the people that existed in the 'Western' churches. In consequence during the communist upheavals in the beginning of the last century, there was such a disrespect from the 'intelligencia', that there was fear the Church of Greece would suffer the same fate as the Church in Russia. It was during this time that God gave Greece Saint Nektarios.
As the story goes, the people of Alexandria clamored for Saint Nektarios to become the next Patriarch not once but twice, but the bishops and clergy were so adamantly against it because his virtue and integrity was threatening to them. As is usually the case, the rational on their part was that his more conservative and less liberal views would be detrimental to the Church so they began to calumniate him to the Patriarch, and Saint Nektarios ended up pennyless and with a ruined reputation and forced to look for work under another jurisdiction.
He underwent great persecution because of the calumny, but in time the truth began to emerge, and the clamor of the people forced the Church of Greece to give him a position. He was thereby placed as the head of the Rizarios School which was also a seminary. His status though was never fully restored and so in a way he had to fight others in almost everything he did, especially in regard to how he taught his students and the establishment of a monastery. God though works in mysterious ways, and so the humiliations and slander against the greatest saint and theologian of our modern era, forced him not only to establish the greatest monastery in Greece today, but more important to help develop true priests and bishops, and thereby save the Church of Greece.
As for monasticism, to understand it's full impact on the Orthodox Church, one has only to watch the 'shorts' on TV inbetween the Greek shows where they show two archeological sites that are in abundance: One is the castles, since Greece has more castles than any place in the world, and the other are the monasteries, which fortunately have continued to exist and were not destroyed by the Ottomans.
Many were run down and empty these past hundred years, but there has been a revival in monasticism so they are being restored and are thriving once more. ..thanks to people like the Elder Dionysius and Abess Amiliani and the rest of the nuns and monks in Greece.