You can do this with cherry-pick. If your history of long_branch looks like this:
A-B <-- master
\
C-D-E-F-G-H <-- long_branch
and you want to move the contents of, say, F through H to a different branch, say, short_branch, which is based off of master:
git checkout master -b short_branch
which gives
A-B <-- master, short_branch
\
C-D-E-F-G-H <-- long_branch
then... (note that the commit range is E..H; the left side is non-inclusive for the range)
git cherry-pick E..H
which gives:
F'-G'-H' <-- short_branch
/
A-B <-- master
\
C-D-E-F-G-H <-- long_branch
Note that I'm referring to the new commits as F', G', H' - this is because while they will contain the same effective changes as F, G, and H, they won't be the actual same commits (due to different parents + commit times).