Undoubtedly both. Definitely Catholic and most probably catholic.

But that is a discussion for theologians and philosophers and not to be addressed here. However, the question is posed to illustrate a linguistic point. Depending on style and interpretation, capitalization in English does matter. In short, the sentence is used to illustrate what a difference a “cap” can make (with apologies for the pun.)

Oxford Dictionaries online offers the following definitions:

Catholic (adjective) Of the Roman Catholic faith. Of or including all Christians. Relating to the historic doctrine and practice of the Western Church; (noun) A member of the Roman Catholic Church.

catholic (adjective) Including a wide variety of things; all-embracing.

There are differences in style, of course, depending on which dictionary or stylebook you use as your preferred reference book; both or neither vary in casing. But most reference books differentiate between the use of the adjective (or noun) related to the Roman Catholic faith and the general meaning of all-embracing or universal, usually by capitalizing the first meaning.

If these were the only pairs in our language, English would be simpler. But there are many. In fact, while on the subject of themes papal, “see” also the entry on the see, as in the Holy See, which is most often capitalized.

See (noun) The place in which a cathedral church stands, identified as the seat of authority of a bishop or archbishop.

And then there is also “sea”, a homophone, and a topic for another time.