Copy *changed/new files only* to a DIFFERENT directory?

If you only need to see which files will be affected, without seeing the differences between them, you can use the --dry-run option to rsync. Let's set up a sandpit for testing:

$ cd /tmp
$ mkdir -p testing/{a,b}
$ cd testing/
$ touch a/hello a/world
$ ls a
hello
world
$ rsync -rv --append-verify a/ b
$ ls b
hello
world

Now perform modifications to the contents of a:

$ echo 123 > a/hello 
$ touch a/abc

Now use rsync ... --dry-run ... to see what would happen:

$ rsync -rv --append-verify --dry-run a/ b
sending incremental file list
abc
hello

sent 103 bytes  received 22 bytes  250.00 bytes/sec
total size is 4  speedup is 0.03 (DRY RUN)

We can see no changes were actually made to b:

$ ls b
hello
world
$ cat b/hello
$

If you need to see the differences between the directories you can use diff:

$ /bin/diff -aurN a b
diff -aurN a/hello b/hello
--- a/hello 2018-12-13 08:16:23.376761456 +1100
+++ b/hello 2018-12-13 08:16:11.306761686 +1100
@@ -1 +0,0 @@
-123

If b is on a remote box and you need to see the differences, you'll need to create a local copy of b and then you can diff.

I believe a better answer is in https://serverfault.com/a/508272/173599. Here I quote the relevant command:

rsync -aHxv --compare-dest=folder2/ folder1/ folder3/

To compare folder1 with folder2 as destination, but copy instead in folder3.