I think that the Orthodox have been declining for the last 700 years because they, more than the Western Church, have born directly the brunt of Islamic and Communist domination.
The European west had been invaded several times in the past by infidels of all stripes. As the Roman Empire collapsed, marauding Germanic tribes professing an Arian form of Christianity sacked Rome and ravaged the imperial cities. Attila the Hun himself penetrated deep into Italy and almost sacked Rome but was dissuaded from doing so by Pope Leo the Great in 452 AD. The Muslims invaded and conquered Spain in the 8th Century and it would be another 700 years before they were expelled. Meanwhile Muslim armies threatened the Byzantine Empire and the forces of Christian Europe waged a series of military campaigns known collectively as the Crusades to keep them at bay. The Muslim forces eventually overpowered the Byzantines and conquered them after the Eastern Churches reneged on their acceptance of the Council of Florence which would have healed the Great Schism. They had been turned back at the naval Battle of Lepanto in 1571 by the outnumbered CATHOLIC forces led by the Spanish. No Protestant monarchs lifted a finger to help despite urgent pleas from the Pope. All of Catholic Europe prayed the new devotion known as the Rosary petitioning God for victory in that battle. Muslim forces continued their imperialistic advances and reached as far as Vienna itself before they were turned back in 1683! After that, they nevermore threatened western Europe.
The Communist menace had plagued both east and west. The Communist dominated government in Portugal in 1917 was the site of the Fatima apparitions where the miracle of the "Dance of the Sun" was seen by thousands, including the reporters for the Communist newspaper who had come to scoff. Communist regimes were ousted in both Brazil and Austria after WWII due in large part of Catholic activists. The most heavily Catholic counties in the old Communist block were Hungary, Czechoslovakia, and Poland. All three of them actively resisted the Communists and were inspired in doing so by their Catholic faith. Cardinals Mindszenty and Wyszyński were openly persecuted by the Communists in an attempt to discredit the Church. Pope Pius XII who had done so much to help war refugees -- Jewish, Christian, and otherwise -- and who was named a righteous-gentile by the Israeli government when he died in 1958 came under slanderous attack by the Communist Rolf Hochluth in his scurrilous play "The Deputy" which we now know was part of a KGB plot against the Church. And the attempted assassination of Pope John Paul II was most certainly linked to the Bulgarian Secret Service acting as surrogates for KGB policies.
Don't tell me that the Latin rite has not "born directly the brunt of Islamic and Communist domination." The Catholic, Apostolic and Roman Church has come into direct conflict with both the Islamic and Communist oppressions and not only survived but won out in the end!