Radically different attack styles would be phenomenal so that you have to completely adapt your strategy to fit the dragon.
Air dragon will work similar to the scuttle crab and run away from you all along the river area, but attack you as he sweeps through.
Earth dragon will knock everyone back and create walls to block you off in various directions. Could cause you to be walled OUT of the pit away from the dragon (while he continues to attack you over the wall), or could wall you IN the pit with the dragon, suffering his Rammus ultimate style AoE damage.
Fire dragon will ignite the ground in areas, causing you to need to reposition. Damage over time if you stand in the fire AND enhanced damage from all sources (including dragon's other attacks). He will change targets regularly, trying to keep a strong damage over time component active on everybody in his aggro list.
Water dragon spawns up mini-dragon allies. Or even periodically splits into mini-dragons. Mildly akin to the Zac passive, but they all attack you as well, and when you kill all of them they re-combine for you to continue fighting the major lizard.