The trend is going both ways. Some songs written by protestants have made it into the songbooks but some of the catholic hymns have made it into the protestant hymnals as well. On Eagles Wings, Be Not Afraid are 2 that come to mind.
Our hymnal has several songs that I recognize from my Methodist days. To be honest I still think they are the best but that is just my opinion and probably because that is what I grew up with.
DISCLAIMER: Catholic Answers has turned over the archive to Catholic-Questions.org and no longer owns, manages, or moderates the forums. For additional apologetics resources please visit www.catholic.com.