If a weapon doesn't have Thrown property it's treated as an improvised weapon and deals 1d4 damage. I believe you also add Strength modifier to the damage.
If a weapon has Thrown property it uses same as if you were performing a melee attack with it.
If you're throwing a heavy weapon from high ground it also deals AoE damage around where it lands. I'm having a hard time finding the exact ruling on the internet, but seen it referenced multiple times.
I'm a bit confused cause you're talking about great weapons in one place, but then you're providing an example for handaxe. Are the barbarian and eldritch knight attempting to throw the same item?
