You can have a look there: https://askubuntu.com/questions/111495/how-to-diff-multiple-files-across-directories, especially Rinzwind's answer which stipulates that you can do directly
diff -qr Folder1 Folder2.
The other solutions are only useful if you want to merge the results.
If you can run GUI application, the best solution would be to use meld or kdiff3.
Another solution would be to use a version control software. For example, with git, you can do:
$ cd Folder1
$ git init
$ git add .
$ git commit -m "First commit"
$ rm -rf *
$ cp -r /PATH/TO/Folder2/* ./
Then, you can use
git status or
git diff to see the differences. For this solution, you may want to do a backup first. Be aware that
rm -rf * do not delete dot files.
Finally, you could have a look to this
vim plugin (I haven't tried it yet): https://github.com/will133/vim-dirdiff. I am sure such plugin also exist for