Whilst they both commercialised the music, The Original Carter Family were singing songs from their own background and their own roots they had absorbed the music it was part of their upbringning.
Lonnie was orignally a jazz banjo player
Donegan was born in Bridgeton, Glasgow, Scotland, on 29 April 1931. He was the son of an Irish mother and a Scots father, a professional violinist who had played with the Scottish National Orchestra. In 1933, at age 2, he moved with his family to East Ham in East London.
As a child growing up in the early 1940s Donegan listened mostly to swing jazz and vocal acts, and became interested in the guitar. Country & western and blues records,and recordings particularly by Frank Crumit and Josh White.
In my opinion this is evident in the difference of the styles.
Lonnies perfomance of the song in my opinion illustrate the difference in their roots, nothing wrong with Lonnies version, but it does not have the same strength of appalachian roots, as the OriginalCarter Family