Here's a script which shows what you really want: after git fetch, it shows the difference between local and remote branches, thus you will know what you have to do (pull, push, rebase, etc.). Put the directory of it to somewhere on your PATH and you can use it as git fetch-log.
#!/bin/sh
# git-fetch-log: Ultimate git fetch-log
#
# It shows the diferences of `local...remote` if both side exists and there
# are differences. Useful to find out what you have to do: `merge`, `rebase`,
# `push`, etc. The arguments passed to log.
#
# Place it somewhere on Your `$PATH` and execute by the `git fetch-log`
# command.
#
# EXAMPLE OUTPUT
# ============================================================================
#
# ==== branch [behind 1]
#
# > commit 652b883 (origin/branch)
# | Author: BimbaLaszlo <bimbalaszlo@gmail.com>
# | Date: 2016-03-10 09:11:11 +0100
# |
# | Commit on remote
# |
# o commit 2304667 (branch)
# Author: BimbaLaszlo <bimbalaszlo@gmail.com>
# Date: 2015-08-28 13:21:13 +0200
#
# Commit on local
#
# ==== master [ahead 1]
#
# < commit 280ccf8 (master)
# | Author: BimbaLaszlo <bimbalaszlo@gmail.com>
# | Date: 2016-03-25 21:42:55 +0100
# |
# | Commit on local
# |
# o commit 2369465 (origin/master, origin/HEAD)
# Author: BimbaLaszlo <bimbalaszlo@gmail.com>
# Date: 2016-03-10 09:02:52 +0100
#
# Commit on remote
#
# ==== test [ahead 1, behind 1]
#
# < commit 83a3161 (test)
# | Author: BimbaLaszlo <bimbalaszlo@gmail.com>
# | Date: 2016-03-25 22:50:00 +0100
# |
# | Diverged from remote
# |
# | > commit 4aafec7 (origin/test)
# |/ Author: BimbaLaszlo <bimbalaszlo@gmail.com>
# | Date: 2016-03-14 10:34:28 +0100
# |
# | Pushed remote
# |
# o commit 0fccef3
# Author: BimbaLaszlo <bimbalaszlo@gmail.com>
# Date: 2015-09-03 10:33:39 +0200
#
# Last common commit
fmt='ref=%(refname:short); up=%(upstream:short); t=%(upstream:track); ts=%(upstream:trackshort);'
git for-each-ref --shell --format="$fmt" refs/heads | \
while read entry; do
eval "$entry"
if test "z$ts" != 'z' && test "z$ts" != 'z='; then
echo -e "\n==== $ref $t\n"
git --no-pager log --graph --left-right --decorate --abbrev-commit --date-order --boundary $@ $ref...$up
fi
done
https://gitlab.com/bimlas/home/blob/3fb207cdfe57593a78abe30150a3bc40b242e26a/linux/home/.gitconfig_files/custom_commands/git-fetch-log