I don't mean to preach, but the beauty of a *nix environment is the diversity of tools. Unfortunately I'm not aware of a software package that does what you ask for, but it can be done with a script. Hopefully, this example will help you write such a script.
We have a couple of folders with multiple files in them (permutations of 0-5 x 0-5).
$ ls new/ |sort | column -x -c 50 | sed 's/\t/ /g'
00 01 02 03 04 05
10 11 12 13 14 15
20 21 22 23 24 25
30 31 32 33 34 35
40 41 42 43 44 45
50 51 52 53 54 55
I removed seven random files from old
and the new
folder has 7 "new" files in it now:
$ find . -type d -exec sh -c 'echo -n {} " "; ls {} |wc -l' \;
. 2
./new 36
./old 29
Rsync (is a grand tool for copying files and making two folders alike) can isolate these new files:
$ rsync --size-only --out-format=%f -rin new/ old/
new/05
new/15
new/21
new/22
new/35
new/54
new/55
These file names can be fed into an archiving tool such as tar after we copy them to a new location:
$ mkdir diff/new
$ rsync -r --size-only --compare-dest=../../old/ new/ diff/new/
$ tar -C diff -czf diff.tar.gz .
And the contents of the archive are our new files:
$ tar tf diff.tar.gz
./
./new/
./new/55
./new/54
./new/35
./new/05
./new/22
./new/15
./new/21