In my opinion, zombies or skeletons or any undead counterparts should have are the following 4 abilities;
-Immunity, to poison, fire, and hazards has such.
-Cannibalize, allows mightier undead (with HP) to feed upon fallen corpses and heal themselves.
-Revival, any undead or corpse can by revived with presence and the power of greater evil, like necromancers, Chtulhu, devils, leeches etc... (also, if the undead/corpse had any armor/weapons with it, they are still equipped).
-Death Knight, heroes can also be revived by evil forces, in this case, they become Death Knights which are more trained then normal undead do their previous life has heroes. They are soul bounded to their weapon, which gives them the Soul Weapon aura. If they lose their weapon or its destroyed, the Death Knight is also destroyed.
PS: You must not forget that when undead come together, they become stronger, also, if they are under command of a necromancer/lich/evil entity, they are pretty much unstoppable.
Good enough? You can give whatever stats you want them to have, if you see that in a game they are to many or to powerful, reduce their stats or create rules that make the game harder to play for the undead.
Hope I helped