The main difference between Methodist and Catholic hymnals is the type and the arrangement of the repertoire by the liturgical calendar. Since Methodists have two Sacraments, and Catholics have seven, music in each denomination's hymnal corresponds to these Sacraments and other holy days and events that are relevant respectively.
Another major difference is the history behind each denomination's hymnal. The Catholic hymnal is a fairly recent invention, incorporating church folk music from the late 19th century and contemporary hymns that have transcended denomination, such as popular Christmas hymns.
Prior to the formation of Vatican II in 1959, Gregorian chant was (and remains) the official sacred music of the Roman Catholic Church. Most Catholic hymnals, as it were, are combinations of church folk song, Gregorian chant, popular holiday hymns and contemporary songs by notable gospel composers, such as Gloria and Bill Gaither.
The idea of new Catholic hymnals coincided with the formation of Vatican II and an intention to renew interest in the church among seasoned parishioners and prospective church members. Some of the elements of worship that hymns address in a Catholic hymnal echo those in a Methodist hymnal, such as offertory selections, processional hymns and closing songs.
However, some Catholic hymnals may also contain all of the congregation's music for Mass, such as the gospel of acclamation, the doxology, the "our Father" and a post-Communion hymn. Catholic hymnals also contain hymns that speak directly to the sainthood of the Blessed Virgin, such as the hymn "The Virgin Mary Hath Conceived."