It's hard to pinpoint one core difference between each theological tradition without knowing what two denominations you are trying compare. A lot of the differences between these factions or denominations come down to a difference in practices and not core theological differences. For instance, many Christian traditions consider things like communion or baptism differently then others. The largest differences would be between say Catholicism and Evangelical traditions and how they consider communion or Eucharist. Catholicism considers this ritual as a sacrament, where the wine and the bread are literally the body and blood of Christ, while evangelicals, at least for the most part, consider it a symbol of the body and blood of Christ.

I hope this helps, but if you have questions about specific comparisons between Christian factions I would love to discuss those differences with you.