Dave Webber and Anni Fentiman gave a class in harmony singing at Pinewoods Folk Music week last summer. For the first session, they played several examples of English groups' harmony styles taken from a wonderful Fellside CD called "Voices in Harmony", and compared and contrasted the styles. The groups were The Watersons, Swan Arcade, Regal Slip and Artisan. Since Dave and Anni knew the people in all four groups, they were able to describe how each arrived at the arrangements they used.
The Watersons start with a song where everyone knows the melody, and they get into a huddle and sing together until everyone finds a place that fits well. Their harmonies come "naturally" from a family group that is used to singing together and improvising.
Regal Slip's harmonies are strongly based on West Gallery hymn singing styles, and are more four-square.
In Artisan, the lead singer devises the entire arrangement, writes out parts for each member, and each person learns just his or her part, as in a strictly classical or art song composition.
Finally, in Swan Arcade, Dave said that Jim Boyes and Heather Brady would sing their harmonies/melodies against each other and Dave Brady was a "wild man" who would add an element of chaos to the mix, resulting in really neat improvisations in the overall sound.
As far as tradition goes, the Watersons and Regal Slip's harmonies are probably more "traditional" than the highly arranged compositions of Artisan or the avant-garde meldings of Swan Arcade. Which groups you enjoy is more a matter of personal taste than one way being better than any other - I myself prefer the rowdiness of the Watersons' free-for-all and Swan Arcade's improvisations to the more stylized compositions of the other two groups.