Do any denominations rank the apostles? Many Christian denominations hold the primacy of Peter as doctrine.  That is, they believe that Peter was the most prominent, authoritative, influential, and/or prestigious of the twelve apostles.  Various scriptual arguments are advanced in support of this belief, including Jesus's so-called Selection of Peter (Matthew 16:18) and fact that he is always named first when the apostles are listed.   The Roman Catholic Church bases its claim of the primacy of the Bishop of Rome over other bishops on the primacy of Peter.

I am wondering whether, among those denominations that recognize the primacy of Peter, any of them assign a rank to each of the other eleven apostles.  The various listings of the apostles given in the New Testament are not consistent in their ordering, except that Peter is invariably first and Judas Iscariot is always last (if he is mentioned at all).  Do any churches make an explicit statement to the effect of, "Peter is the most important apostle, Andrew the second-most important," and so on for all twelve?  If not, have any prominent theologians from any major denominations (say, the Roman Catholics) argued for such a ranking?
The Church of Jesus Christ of Latter Day Saints does not "rank" apostles, but believes that Peter, James, and John were given more authority than the other apostles. In particular, Peter, James and John made up what was known a First Presidency (source), which means that they were tasked with directing the work of the other appostles.

Note that this does not make Peter, James and John "more important" than the other apostles. They were all assigned important work. They were just the leaders.

I do not of any type of "rankings" between the other apostles though, except maybe by "seniority". When the president of the Church dies, the most senior apostle takes over his work until a new president is called.

At the time of this question, the first presidency now consists of President Nelson, President Oaks and President Eyring, who fill the vacancy left by Peter, James and John (and all the other first presidencies in between).