+1  A: 

I believe the answer here is to execute your diff at the parent directory. Then use patch -p1 to strip this first segment. I believe this is why the strip option of patch actually defaults to 1 rather than 0. E.g. to use your example from above

$ mkdir copyfrom
$ mkdir copyto
$ echo "Hello world" > copyfrom/myFile.txt
$ diff -Naur copyto copyfrom > my.diff
$ less my.diff

diff -Naur copyto/myFile.txt copyfrom/myFile.txt
--- copyto/myFile.txt    1970-01-01 12:00:00.000000000 +1200
+++ copyfrom/myFile.txt    2010-10-19 10:03:43.000000000 +1300
@@ -0,0 +1 @@
+Hello world

$ cd copyto
$ patch -p1 < ../my.diff

The only difference from your example is that I've executed the diff from the parent directory so that the directories being compared are at the same level.

EdC