Pathfinder 1E Ranger Favored Enemy Bonus for Augmented Enemy

If a Ranger has Favored Enemy (Giant) and fights an Undead Ogre, should the attack and damage bonus v giants still work or tough luck?

It depends on the type of undead. Per this a zombie does not gain the augmented subtype, so its type changes from giant to undead, with the result that mechanic affects that are based upon type (giant) would no longer work upon the zombie ogre. However, per this a wight does gain the augmented subtype. As a result, mechanic affects based upon either type (giant or undead) would affect the wight ogre. Just check the 'type' section of the undead template you are applying to see if it allows the final result to count as 'augmented' or not.