Both the Roman Catholic and the Eastern Orthodox Churches claim to be THE Catholic Church. That's the important theological point.
Otherwise, capitals are really an incidental question of English style and usage, since the original documents of the early Church, in both Greek and Latin, used either (a) all capitals or (b) a cursive style with no capitals. Thus, the Nicene-Constantinopolitan Creed (whose final version didn't come about until Chalcedon) was probably written in ALL capitals with no punctuation marks or spaces between letters and words.
All printed translations of the Creed I have read (in Latin, French, German, Romanian and English) capitalize all of the adjectives. Thus, all of the versions of the Creed in my possession say: "One, Holy, Catholic, and Apostolic Church." But, like I said, that's just a reflection of the modern editor's typographical predilections based on whatever standard of English usage he favors. One can decide to capitalize or not capitalize whatever one wants.
Thank you for enlightening me. I guess I need to catch up on my Orthodox education.