It all depends on what you mean.
If by "Jewish" you mean adherence to a legal/ceremonial/ritual system and a rejection of antinomianism, then I suppose the Catholic Church would be considered (lehavdil) "Jewish," and antinomian Protestants often accuse the Catholic Church of being a "Judaizer" for this reason. Furthermore, the Roman (as opposed to the other ancient churches) has a very legal mindset, so I suppose you could say it is more Jewish than (for example) the Eastern Orthodox, though naturally the Orthodox would disagree with that.
However, if by "Jewish" you mean a sentimental attachment to the Biblical/Jewish legal/ritual/ceremonial system and Jewish understandings of a "political" Messiah and a Judaeo-centric interpretation of the Prophets, then the so-called "Hebrew roots" people among the Fundamentalist Protestants are far, far more (lehavdil) "Jewish" than the Catholic Church, and sure enough, Catholics often accuse these people of being "Judaizers."
The Fundamentalist Judaeo-Protestant attachment to Jewish rituals/holidays etc. seems to be out of Biblical sentimentalism, since they all reject the notion that human behavior has anything to do with "salvation." To them, while Jewish ritual does not good, it also does no harm. The Catholic Church OTOH while insisting on the necessity of laws, ceremonies, rituals, calendars, etc., positively forbids the Jewish ones and insists that others have taken their place. Thus it is probably truest to say that no version of chrstianity is "more Jewish" than any other.