This question covers a wide, largely unexplored field. It will not be easy to draw parallels before we know what to choose as a type for comparison in the synagogal liturgy on the one hand, and in the wealth of Christian liturgies On the other. Jewish prayers comprise not only those which were codified and organized as such and may be termed liturgy proper, but also an abundance of another type of prayer which is not official, but where we may yet find traces of the early Jewish prayer. In the Christian liturgy the best witness will not be the Roman, but some of the Eastern rites, especially the Coptic and Syriac.
Again similarities with the synagogal prayer will be found more easily in the Divine Office than in the Mass. Although we know very little about the origins of the breviary and how it was constituted, one notices a convergence of private and monastic piety, as well as liturgical tradition, part of the latter going back to the Synagogue.