When I was at uni, I was more evangelical because that was the tradition most people my age belonged to. While I was there I had a Roman Catholic boyfriend and I got talking a lot with an Anglo-Catholic chaplain. They helped me begin to see the different emphases between more 'evangelical' and more 'catholic' theology and spiritually.
I found a book about Anglicanism at one point that set out in two columns the main differences in spirituality between the evangelical and catholic wings of the Anglican church. Without wanting to go into too much in-depth theology, here are the main differences in spirituality I've read about and observed myself:
As a generalisation, evangelicals focus more on 'I' and catholics focus more on 'we'.
A lot of songs in evangelical churches use 'I' and 'me' in them to help people appreciate the personal forgiveness and intimate relationship Jesus offers us. While evangelicals pray in groups a lot, the daily prayer life of individual evangelicals tends to focus on a daily "quiet time" that focuses on that individual's personal walk with God and response to God. Catholic prayers and songs tend to use 'we' and 'us' more, and almost every gathering or service makes sure to have an element of praying for the wider community and Church and world. Even when more catholic Christians pray on their own at home, there is still a sense of 'connection with the wider Church' about it. They intentionally use the same prayers and same Bible readings as other Christians on any given day. For catholics, to be a Christian isn't just to be someone who has responded to Jesus for themselves, it's very much to be a member of the worldwide Church.
Evangelicals focus on the fact that Jesus died for you personally (not that catholics would disagree with that). The more catholic focus regarding Jesus' death seems to be on how Jesus died to reconcile the whole world, and not just all people but all creation to himself.
When evangelicals talk about "the Word of God", they mean the Bible. When catholics talk about "the Word of God", they mean Jesus himself. The Bible is extremely important in catholic thought because it points to and helps us get to know the Living Word of God Himself.
Evangelical spirituality places a lot of emphasis on the Bible, and on Bible study, good preaching, teaching, courses to help people understand their faith. The talk (sermon) is the highlight of the service, and when an evangelical is looking for a church to join, good preaching is likely to be one of their big concerns. Catholic spirituality, on the other hand, places a lot of emphasis on the Eucharist. 'More catholic' churches celebrate the Eucharist every Sunday as their main service, and while the Eucharist contains Bible study in the readings and sermon, the receiving of Holy Communion (the receiving of "the living Word of God" directly into our bodies) is the highlight of the service. The intimacy of our relationship with Jesus is particularly reinforced in Holy Communion in more catholic thought.
As an overgeneralization, evangelical spirituality tends to be a bit more words based and intellect based - although charismatic spirituality emphasises experience and personal encounter with God. Catholic spirituality wants to use as many of the five sense as possible in worship, hence the incense and bells and use of the body (kneeling and making the sign of the cross for example).
That's just a few of the main differences I'm aware of so far as prayer and worship are concerned.
