The US ("west offshoots" in the graph, but south america can be mostly ignored until the later 20th century) grew faster then western Europe, but they only really diverged before WW1.
Europe never really recovered from the devastation that was WW1 until the 50ies.
Interesting graphs:
http://krusekronicle.typepad.com/kruse_kronicle/images/2008/...
https://ourworldindata.org/wp-content/uploads/2013/11/long-t...
The US ("west offshoots" in the graph, but south america can be mostly ignored until the later 20th century) grew faster then western Europe, but they only really diverged before WW1.
Europe never really recovered from the devastation that was WW1 until the 50ies.
WW2 helped the US out of a big dip though.