A diamond sword does 7 damage normally, and each level of Smite/Bane adds 2.5 damage to their respective enemy types. Zombies have a little innate defense, but that essentially means you can kill a zombie with two full power swings of a Smite II sword. A Smite IV sword should do 17 damage and a Smite V sword should do 19.5 - so both would take two swings or one critical swing to kill.
But keep in mind:
- Zombies and skeletons can spawn with armor, potentially making some cases where Smite V continues to kill in two hits but Smite IV just barely misses the mark, or Smite V's critical is a one-shot but Smite IV fails to kill.
- Smite V doing 19.5 damage means Fire Aspect following your attack is enough to one-shot an unarmored zombie or skeleton. Won't do shit against Nether enemies though.
- 1.9 nerfed Sharpness V to only add 3 damage for a total of 10 on a diamond sword, meaning it'll only two-shot unarmored undead and require two hits to kill a spider even with a critical hit. Zombies and armored foes will all require at least three hits with a Sharpness sword, and unless you want to fight with a Sharpness axe, a Bane sword is your only option to kill a spider with one hit now. (Cave spiders can still be one-shot with a critical Sharpness V sword.)
- If you're doing this for mob grinder purposes, a beacon with strength on could change numbers further. Strength I will allow Smite IV to do 20 damage in one hit, for example, but it will fail to one-shot a zombie because of its slight innate armor. Smite V won't care and will murder the zombie all the same.
But keep in mind:
- Zombies and skeletons can spawn with armor, potentially making some cases where Smite V continues to kill in two hits but Smite IV just barely misses the mark, or Smite V's critical is a one-shot but Smite IV fails to kill.
- Smite V doing 19.5 damage means Fire Aspect following your attack is enough to one-shot an unarmored zombie or skeleton. Won't do shit against Nether enemies though.
- 1.9 nerfed Sharpness V to only add 3 damage for a total of 10 on a diamond sword, meaning it'll only two-shot unarmored undead and require two hits to kill a spider even with a critical hit. Zombies and armored foes will all require at least three hits with a Sharpness sword, and unless you want to fight with a Sharpness axe, a Bane sword is your only option to kill a spider with one hit now. (Cave spiders can still be one-shot with a critical Sharpness V sword.)
- If you're doing this for mob grinder purposes, a beacon with strength on could change numbers further. Strength I will allow Smite IV to do 20 damage in one hit, for example, but it will fail to one-shot a zombie because of its slight innate armor. Smite V won't care and will murder the zombie all the same.