[Idiom] "Cry one's heart out" or "Cry one's eyes out"?

[Aamir Tariq]

I have heard "cry one's heart out" which definitely means to cry hard. But today I saw "cry one's eyes out" written under the title of "American idioms". Does it mean the same thing? By "eye" it sounds like shedding lots tears through/out of one's eyes. Which one of them is more common in your versions of English? I mean in British English, in American English and off course in Australian English?

I am not sure if "Cry one's heart out" is more common in British and "Cry one's eye out" in American English.

Regards,
Aamir the Global Citizen.

 

[Rover_KE]

I would only use 'eyes' (BrE).

 

[jutfrank]

cry one's eyes out is a lot more familiar to me.

 

[GoesStation]

Cry one's eyes out is common in AmE. Heart would sound odd but understandable.