The lightning staff is a powerful tool for high DPS and decent sustain. It comes with many benefits, but also has its limitations. This staff type has the chance of applying the concussion status effect. Which can be triggered by dealing shock damage. Concussed enemies are set off-balance using the wall of elements (wall of lightning), activating minor vulnerability. This minor debuff is applied on the target and increases damage taken by 8%. Which can greatly increase your damage in dungeons and PVP situations. Minor vulnerability however can also be obtained by equipping the Infallible Mage set or Wise Mage set. Which both have the five-piece bonus of applying minor vulnerability after damaging your enemy with a fully-charged heavy attack. Besides increasing your damage on an enemy, the heavy attack is considered a DoT. Which increases the chance of proccing sets that activate by dealing damage (e.g. Valkyn Skoria set). A fully-charged heavy attack will also deal a small AoE damage effect and, similar to the restoration staff, returns magicka to your magicka pool.
The frost staff is a destruction staff of a different type. The frost staff can be used for DPS builds, but mainly has the function as tank equipment. A fully-charged heavy attack will taunt the target, forcing it to attack you (the caster). Also it has the chance of applying the chilled status effect. This status effect can trigger minor maim on an enemy. This debuff will result into reducing the damage dealt by 15%. The Knightmare set and Wizard's Reposte set both trigger the same minor debuff. The frost staff is most used in pvp for snaring and rooting enemy players. Blocking with the frost staff will cost you magicka, just like blocking with a shield costs stamina. In PVP this is beneficial for magicka builds, since it will reduce the strain on the already low max. stamina pool.
The flame staff is a powerful weapon of choice. It mostly focuses on high DPS. All flame damage has the chance of applying the burning status effect. Which basically is a small DoT and adds to your DPS. Combining the wall of elements (wall of flame) with the burning status effect will greatly improve your DPS. Because the wall of elements will deal more damage to burning targets. Especially magicka dragonknights will benefit from the flame staff. The Burning Spellweave set will also have a higher up-time whilst using the flame staff.