Zombies, by definition, have no intelligence whatsoever. The Borg are intelligent - collectively so. (Plus, it is possible to leave the Collective and become individual again.) Therefore, the Borg are not zombies.
And for the last time, the Federation is nothing like the Borg, because (among other things) the Federation never forces worlds to join. They have the right to make their case, so to speak - to convince a world of the benefits of membership. But the ultimate choice is up to that world. If they don't want to join, they aren't forced to. You don't see the Borg offering a choice, do ya?