It's not clear to me what point you're trying to make, but the second one gives an error: "-e expression #1, char 2: unknown command: `''", because it's getting

It's not clear to me what point you're trying to make, but the second one gives an error: "-e expression #1, char 2: unknown command: `''", because it's getting a single argument containing a quote. Removing the quotes gives "-e expression #1, char 10: unknown option to `s'", because "s/a/b/g -f" is not a valid sed command. And to illustrate my point about env, sed for me is in /bin. But "#!/usr/bin/env sed -f" doesn't work, because it looks for a program named "sed -f".