¿Cuál es la diferencia entre 마음껏 y 실컷 ?Puedes dar oraciones como ejemplo.

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When you talk about your personal satisfaction, they are interchangeable.

e.g.)
I like going to libraries because I get to read books all I want!
(책을 실컷 읽을 수 있어서 도서관에 가는 걸 좋아해요!)

*I chose 실컷 between those two because 실컷 feels slightly more liberating than 마음껏. But 책을 마음껏 읽을 수 있어서 has no problem at all as well.

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When you talk about allowing people something, especially in formal situations, 마음껏 seems to be preferred.

e.g.)
Feel free to ask me questions.
(마음껏 질문하세요 or 얼마든지 질문하세요)

In this case, 마음껏 sounds right and 실컷 질문하세요 sounds a little bit wild. 실컷 almost reminds me of some kind of disorder (one bit too liberating).

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However, if it's your best friend that you allow something, 실컷 has no problem at all, or is preferred.
e.g.)
Will you come over this weekend? I'll let you play games on my XBOX all you want.
(이번 주말에 우리 집에 놀러 올래? 게임 실컷 하게 해 줄께)


P.S.
'어느 써야겠나요?' is not right :)
It should be 어느 것을 써야 하나요? or 어느 것을 써야 되나요? or 어느 것을 써야 할까요? or 어느 것을 써야 좋을까요? (All mean 'Which one should I use?')