If you really wanted to make a Christian comparision, you could compare the liberal Jewish groups to liberal Catholics and mainline Protestants, who tend to give their religion lip service, but follow popular culture in terms of values and day to day life.
You could compare Orthodox Judaism to traditional Catholics and Evangelical Christians, who actually follow their religions’ teachings in their day to day lives.
As far as Litvaks and Chasidim go, you could compare Litvaks to Baptists in their spiritual approach and Chasidim to Pentecostals.
In terms of Islam, the Sunnis are best compared with Litvaks, and the Shiites are best compared with Chasidim in terms of their approach to spirituality.
(L’havdil)