What traditions of the Catholic and Jewish church are similar?

Answer 1

Judaism is not a church, it is a religion; just as Catholicism is a religion. Catholicism is basically Judaism fulfilled. All of the original Christians were Jews who saw in Our Blessed Lord, Jesus Christ, the promised Messiah. Our Blessed Lord fulfilled over 300 Old Testament prophecies of the promised Messiah to the letter; in short, every single one of them was fulfilled with the coming of Jesus of Nazareth. Our Blessed Lord, in fulfilling the Old Testament brought it to its logical conclusion and instituted the final and complete covenant with the entire world. In fulfilling the Old Testament, we take into account that there are, I believe 613 commandments in the Torah, St. Thomas Aquinas divides these into three categories, moral, legal, and prophetic. For instance, the Ten Commandments are ten examples of moral laws in the Old Testament, and these are forever valid. Legal commandments may or may not be valid depending on the government where you live. The ceremonial precepts (the prophetic commandments) were to preshadow the Messiah, it is a mortal sin to observe any of these, as it would be saying that you don't believe the Messiah has come. The latter would include the dietary laws and such like.

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In addition to the moral commandments, there is the matter of prayer, and Christian prayer is very much based on Jewish prayer. To this day the prayerbook of the Christian Church is the book of Psalms, which is prayed throughout the day in the Divine Office and at a Mass. The Mass itself, the first part is based on the synagogue services of readings and homily; the second part is based on the Passover, and its meal.

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In short, there is very little in Catholicism which does not have its roots firmly embedded in Judaism, which is no surprise as this is how God went about revealing Himself.

Answer 2

There are only superficial similarities.
Judaism has no pope, no ranks at all, no "Church" and no structure above the level of the local synagogue. Judaism also no longer has a functioning priesthood since the year 70 CE, and even when it did, it was nothing like the Catholic Priesthood, which violates the Jewish understanding of the commandment of Genesis 1:22 (be fruitful and multiply).

Even though Catholicism believes it is based on Judaism, the similarities are few:

• Prayer services are often in another language (Latin for Catholics, Hebrew for Jews).
  
• Prayers are mostly sung
• There is ritual repetition of prayers, though Catholics do this much more than Jews.
• There is standing and sitting during prayers (but Jews do not kneel).
• The catholic altar looks vaguely like a bimah in a synagogue