I missed something, namely a fifth author:
Merlin returns in CS Lewis' Ransom Trilogy;
advanced technology stops working in SM Stirling's Change series;
advanced technology stops working because Merlin returns in Peter Dickinson's Changes Trilogy.
(At least, I have been told that Merlin returns in the Changes Trilogy.)
"Four Authors" compares:
Lewis and Tolkien;
Anderson and Tolkien;
Anderson and Stirling;
Stirling and Tolkien.
My advice: read them all.