I believe that this is equivalent to what you are looking for:

git checkout better_branch          # This is the branch whose commits you want to keep
git merge --strategy=ours master    # keep the content of this branch, but record a merge
git checkout master                 # You want to **lose** all changes on this branch
git merge better_branch             # fast-forward master up to the merge

See: https://stackoverflow.com/a/2763118/1290781