Being the weakest of the 6, there is not much use for this shield. This shield has no offensive bonuses. It is obtained as a drop from the Corporal Beast. There is no special effect.
This shield is made by using a Holy Elixir on a regular Spirit Shield. This shield has no offensive bonuses. It has the Same base stats as the Spectral and Arcane. There is no special effect.
This shield is made by using a Spectral Sigil on a Blessed Spirit Shield. This shield has no offensive bonuses. The Spectral is the best in slot for mage defense (+30), making it a good choice for tanking against magic attacks. Its special effect reduces the effect of all prayer draining attacks by 50%. This is not active in PvP. This makes the shield useful at bosses that drain a lot of prayer, like Cerberus and Scorpia.
This shield is made by using an Arcane Sigil on a Blessed Spirit Shield. The Arcane is best in slot for mage attack (+20), making it a good choice for anywhere that mage is used. There is no special effect.
This shield is made by using an Elysian Sigil on a Blessed Spirit Shield. This shield has no offensive bonuses. (Contrary to popular belief, it is not a range shield). It shares the same stats as the Divine Spirit Shield. The Elysian has a hidden effect that has a 70% chance to block 25% of the incoming damage from an enemy's attack. This equates to blocking an average of 17.5% of all incoming damage. The Elysian does not drain prayer points. This makes the Elysian a great choice for tanking and afking in PvM.
This shield is made by using a Divine Sigil on a Blessed Spirit Shield. This shield has no offensive bonuses. It shares the same stats as the Elysian Spirit Shield. The Divine has a hidden effect that blocks all incoming damage by 20%. (Not 30%, which is a common misconception.) When this effect takes place, prayer points are drained. This means that the Divine and Elysian are much closer in performance than many think.
Note: The Divine Spirit Shield's effect now acts as an Elysian Spirit Shield in PvP (both in the wilderness & outside), having a 70% chance to reduce 25% damage at no prayer point cost. The Divine Spirit Shield effect in PvM remains unchanged (always 20% damage reduction and 15% of the damage is removed from your prayer points) Note that the Divine Spirit shield effect now works in the Duel Arena when prayer is disabled, as it no longer uses prayer points in PvP.
Elysian and Divine are equal in terms of DPS for Range and Melee as neither of them have an attack or strength bonus.
In my personal opinion, the Elysian is better than Divine everywhere except Corporal Beast. The Divine drains prayer too quickly and it is not worth the additional 2.5% damage blocked. In most situations, with max near max gear, you are better off using a Dragon Defender/DFS, Odium Ward/Dragonfire Ward, or Arcane Spirit shield depending on your attack style. Attack bonuses should almost always be prioritized over Defence bonuses.