The heat of formation (as solids, not solutions, sorry) of FeCl3 is -400kJ/mol versus -342kJ/mol for FeCl2, but the reaction replaces 2 moles by 3 moles.
The reasoning also ignores the fate of chlorine, but it's important besides the iron ions.
Metallic iron too is important. Aggregating it from individual atoms means a huge energy. The heat of formation of the compounds is measured versus their constituent elements in normal state, here solid iron, hence the my comparison at first line holds, but it's conceptually important: comparing only FeCl3 and FeCl2 with atomic iron would neglect that Fe is solid.