Use svn patch.
Case 1: using /usr/bin/patch:
svn diff > $TMPDIR/mypatchfile.patch
cd myOtherCheckOut
patch -p0 < $TMPDIR/mypatchfile.patch
Applies your changes well if there are no added/deleted files through svn add or svn delete
Case 2: using svn patch:
svn diff > $TMPDIR/mypatchfile.patch
cd myOtherCheckOut
svn patch $TMPDIR/mypatchfile.patch
Tracks added and deleted files too.
Note that neither tracks svn moves and renames