It isn’t exactly the same as sed -i, but i had a similar issue. You can do this using perl:
perl -pi -e 's/find/replace/g' file
doing the copy/move only works for single files. if you want to replace some text across every file in a directory and sub-directories, you need something which does it in place. you can do this with perl and find:
find . -exec perl -pi -e 's/find/replace/g' '{}' \;